// Numbas version: finer_feedback_settings
{"name": "Week 3 tutorial", "metadata": {"description": "<p>Tutorial questions focusing upon the Coulomb field, electrostatic potentials and parallel plate capacitors</p>", "licence": "All rights reserved"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", ""], "questions": [{"name": "Coulomb forces", "extensions": [], "custom_part_types": [], "resources": [["question-resources/twopointcharges.png", "/srv/numbas/media/question-resources/twopointcharges.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}], "tags": ["coulomb", "elec", "force", "tut1"], "metadata": {"description": "Simple calculation of a Coulomb force between two point charges to highlight the importance of units and the inclusion of the correct constants.", "licence": "All rights reserved"}, "statement": "<div><img style=\"float: left; width: 200px;\" src=\"resources/question-resources/twopointcharges.png\"/></div>\n<div>\n<p>This question relates to Coulomb&rsquo;s Law, which gives the force per unit charge due to the interaction between stationary charges.</p>\n<p>When providing numerical answers you may express them using scientific notation.&nbsp; Express values to four significant figures and use the values of physical constants as provided in the course notes, and take the relative permittivity of air to be 1.0005.</p>\n</div>", "advice": "<p>If you got the wrong answer, did you remember to</p>\n<ul>\n<li>Convert all quantities to SI units?</li>\n<li>Include the relative permittivity of air (1.0005)?</li>\n<li>Square the distance?</li>\n</ul>\n<p>The $E$-field due to a point charge is</p>\n<p style=\"text-align: center;\">$\\displaystyle{q\\over 4 \\pi \\varepsilon_0 \\varepsilon_r r^2}$</p>\n<p>radially away from the point charge.&nbsp; The force experienced in an electric field is generally $\\vec{F}=q\\vec{E}$, so the force on a point charge, $q_1$ due to another point charge, $q_2$ has a magnitude of</p>\n<p style=\"text-align: center;\">$\\displaystyle q_1 {q_2\\over 4 \\pi \\varepsilon_0 \\varepsilon_r r^2}$.</p>\n<p>Since typically $\\varepsilon_r\\ge1$, any material between the two charges tends to reduce the force relative to the point charges in vacuum.&nbsp; It is important to note that the question asks for the percentage by which the force is reduced, not the percentage of the original force that remains.</p>\n<p>The force due to gravity is $mg$ towards the centre of the Earth, so one can calculate the force due the electric field and work out the mass that when mulitplied by $g$ has the same magnitude.</p>", "rulesets": {}, "variables": {"g": {"name": "g", "group": "Ungrouped variables", "definition": "9.8", "description": "<p>Approximate value for the acceleration due to gravity on Earth's surface (m/s/s).</p>", "templateType": "anything"}, "eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "8.854*10^-12", "description": "<p>Permittivity of free space in F/m.</p>", "templateType": "anything"}, "mass": {"name": "mass", "group": "Ungrouped variables", "definition": "force1/g", "description": "<p>Mass that would balance the force between the charges on Earth (kg).</p>", "templateType": "anything"}, "r1": {"name": "r1", "group": "Ungrouped variables", "definition": "random(0.5..2.5#0.5)", "description": "<p>Distance of the second point charge from the first in cm.</p>", "templateType": "anything"}, "epsmat": {"name": "epsmat", "group": "Ungrouped variables", "definition": "random(4..10#0.1)", "description": "<p>Randomised relative permittivity of material substituting for air (no units)</p>", "templateType": "anything"}, "q2": {"name": "q2", "group": "Ungrouped variables", "definition": "siground(random(0.5..2.5#0.5 except q1),2)", "description": "<p>Magnitude of charge for which the electric field is originating in $\\mu$C, randomised in steps of 0.5$\\mu$C from 0.5 to 2.5$\\mu$C, but different from $q_1$.</p>", "templateType": "anything"}, "epsair": {"name": "epsair", "group": "Ungrouped variables", "definition": "1.0005", "description": "<p>Relative permittivity of air (dimensionless quantity).</p>", "templateType": "anything"}, "force2": {"name": "force2", "group": "Ungrouped variables", "definition": "q1*q2*(10^(-12))/(4*pi*eps0*epsmat*(r1*(10^(-2)))^2)", "description": "", "templateType": "anything"}, "q1": {"name": "q1", "group": "Ungrouped variables", "definition": "siground(random(0.5..2.5#0.5),2)", "description": "<p>Magnitude of charge for which the force is to be obtained in $\\mu$C, randomised in steps of 0.5$\\mu$C from 0.5 to 2.5.</p>", "templateType": "anything"}, "force1": {"name": "force1", "group": "Ungrouped variables", "definition": "{q1}*{q2}*(10^(-12))/(4*pi*{eps0}*{epsair}*(r1*(10^(-2)))^2)", "description": "<p>Coulomb force on one charge due to another, in N, is given by $q_1q_2/4\\pi\\varepsilon r^2$.</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["eps0", "epsair", "epsmat", "force1", "force2", "g", "mass", "q1", "q2", "r1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Force between two point charges", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Using Coulomb's Law, calculate the force on a {q1} $\\mu$C point charge due to the electric field from a {q2} $\\mu$C charge when they are separated by {r1} cm of air.</p>\n<p style=\"text-align: center;\">$|\\vec{F}| =$ [[0]]&nbsp;Newtons.&nbsp;</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "force", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{force1}*0.995", "maxValue": "{force1}*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": "0", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Effect of permittivity", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>By what percentage is the force <strong>reduced</strong> when the air is replaced by a material with relative permittivity, $\\varepsilon_r =\\var{epsmat}$?&nbsp;&nbsp;</p>\n<p style=\"text-align: center;\">The force is reduced <strong>by</strong> [[0]]&nbsp;%</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "percentage", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "(force1-force2)/force1*99.5", "maxValue": "(force1-force2)/force1*100.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Balancing gravitational force", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If in this particular case the gravitational force at the surface of the Earth balances the electric force on the $\\var{q1}\\,\\mu\\text{C}$ point charge due to the $\\var{q2}\\,\\mu\\text{C}$ point charge, what is its mass?&nbsp; Take the accelleration due to gravity at the Earth's surface to be {g} N/kg.</p>\n<p style=\"text-align: center;\">The mass balanced by the electric field force is [[0]] kg</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "mass", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{mass}*0.995", "maxValue": "{mass}*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Coulomb's Law for a pair of charges", "extensions": [], "custom_part_types": [], "resources": [["question-resources/CoulombForce1.png", "/srv/numbas/media/question-resources/CoulombForce1.png"], ["question-resources/CoulombForce2.png", "/srv/numbas/media/question-resources/CoulombForce2.png"], ["question-resources/CoulombForce3.png", "/srv/numbas/media/question-resources/CoulombForce3.png"], ["question-resources/CoulombForce4.png", "/srv/numbas/media/question-resources/CoulombForce4.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}], "tags": ["coulomb", "elec", "field", "force", "mid1718"], "metadata": {"description": "Concepts and calculation involved in the use of Coulomb's Law for both the field and the force, including units and directions.", "licence": "All rights reserved"}, "statement": "<p>This question assesses understanding of the names and units of symbols in the Coulomb equation, the ability to perform calculation of quantities and to evaluate of force directions.&nbsp;&nbsp;</p>\n<p>When providing numerical answers you may express them using scientific notation.&nbsp; Express values to four significant figures and use the values of physical constants as provided in the course notes.</p>", "advice": "<p>The Coulomb field is for a point charge (the equation does not generally apply to all charge arrangements):</p>\n<table>\n<tbody>\n<tr>\n<td>Symbol</td>\n<td>Description</td>\n<td>Units</td>\n</tr>\n<tr>\n<td>$E$</td>\n<td>Electric field strength</td>\n<td>V/m (or N/C)</td>\n</tr>\n<tr>\n<td>$q$</td>\n<td>Point charge</td>\n<td>C</td>\n</tr>\n<tr>\n<td>$\\varepsilon_0$</td>\n<td>Permittivity of free space</td>\n<td>F/m</td>\n</tr>\n<tr>\n<td>$\\varepsilon_r$</td>\n<td>Relative permittivity of medium betweem the point charge and where the field is being established</td>\n<td>none</td>\n</tr>\n<tr>\n<td>$r$</td>\n<td>Distance from the point charge - it's definitely not a radius!</td>\n<td>m</td>\n</tr>\n<tr>\n<td>$\\hat{r}$</td>\n<td>This is the unit radial vector.&nbsp; It is not a displacement (which would have units of m).</td>\n<td>none</td>\n</tr>\n</tbody>\n</table>\n<p>In the calculation of the magnitude of the electric field strength, care has to be taken to correctly account for units.</p>\n<p>From the electric field, a force can be obtained using $F=qE$.&nbsp; For this problem the field has already been obtained, and all that's required is to multiply this by the magnitude of the second point charge.</p>\n<p>Since the charges are opposite in sign, they attract.</p>", "rulesets": {}, "variables": {"q2": {"name": "q2", "group": "Ungrouped variables", "definition": "q2mu/10^6", "description": "<p>Second point charge in C.</p>", "templateType": "anything"}, "q1": {"name": "q1", "group": "Ungrouped variables", "definition": "q1mu/10^6", "description": "<p>Point charge in C.</p>", "templateType": "anything"}, "efield": {"name": "efield", "group": "Ungrouped variables", "definition": "q1/(4 pi eps0 r^2)", "description": "<p>Electric field at the distant point in N/C.</p>", "templateType": "anything"}, "q2mu": {"name": "q2mu", "group": "Ungrouped variables", "definition": "random(1..20 except q1mu*10)*-0.1", "description": "<p>Charge on the second point charge in muC.</p>", "templateType": "anything"}, "rmm": {"name": "rmm", "group": "Ungrouped variables", "definition": "random(1..20)*0.1", "description": "<p>Radial distance from the point charge, mm.</p>", "templateType": "anything"}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "rmm/1000", "description": "<p>Radial distance from the point charge, m.</p>", "templateType": "anything"}, "force": {"name": "force", "group": "Ungrouped variables", "definition": "-efield*q2", "description": "<p>Magnitude of force on second point charge, N.</p>", "templateType": "anything"}, "eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "8.854*10^-12", "description": "<p>Permittivity of free space, F/m.</p>", "templateType": "anything"}, "q1mu": {"name": "q1mu", "group": "Ungrouped variables", "definition": "random(1..20 except rmm*10)*0.1", "description": "<p>Point charge in micro-C.</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["efield", "eps0", "force", "q1", "q1mu", "q2", "q2mu", "r", "rmm"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Coulomb's Law is embodied in the equation&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle \\vec{E}= {q\\over 4 \\pi \\varepsilon_0 \\varepsilon_r r^2}\\hat{r}$.</p>"}, {"type": "gapfill", "useCustomName": true, "customName": "Symbols, their meanings and their units", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: center;\">$\\vec{E}$ is&nbsp;[[0]] with units&nbsp;[[1]]</p>\n<p style=\"text-align: center;\">$q$ is&nbsp;[[2]] with units&nbsp;[[3]]</p>\n<p style=\"text-align: center;\">$\\varepsilon_0$ is&nbsp;[[4]] with units&nbsp;[[5]]</p>\n<p style=\"text-align: center;\">$\\varepsilon_r$ is&nbsp;[[6]] with units&nbsp;[[7]]</p>\n<p style=\"text-align: center;\">$r$ is&nbsp;[[8]] with units&nbsp;[[9]]</p>\n<p style=\"text-align: center;\">$\\hat{r}$ is&nbsp;[[10]] with units&nbsp;[[11]]</p>", "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "DE", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["electric field strength", "electric flux", "charge", "point charge", "permeability", "permeability of free space", "permeability of the material", "relative permeability of the material", "permittivity of the material", "permittivity of free space", "relative permittivity of the material", "radius", "distance from the point charge", "displacement vector", "unit displacement vector", "unit&nbsp;radial vector"], "matrix": ["1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "UE", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["V/m", "N/C", "C", "F/m", "none", "m", "J", "A", "V", "N", "F", "K", "eV", "Pa", "kg", "Hz"], "matrix": ["1", "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Dq", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["electric field strength", "electric flux", "charge", "point charge", "permeability", "permeability of free space", "permeability of the material", "relative permeability of the material", "permittivity of the material", "permittivity of free space", "relative permittivity of the material", "radius", "distance from the point charge", "displacement vector", "unit displacement vector", "unit&nbsp;radial vector"], "matrix": [0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "No - it's a point charge!", "", "", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Uq", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["V/m", "N/C", "C", "F/m", "none", "m", "J", "A", "V", "N", "F", "K", "eV", "Pa", "kg", "Hz"], "matrix": [0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Deps0", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["electric field strength", "electric flux", "charge", "point charge", "permeability", "permeability of free space", "permeability of the material", "relative permeability of the material", "permittivity of the material", "permittivity of free space", "relative permittivity of the material", "radius", "distance from the point charge", "displacement vector", "unit displacement vector", "unit&nbsp;radial vector"], "matrix": [0, 0, 0, 0, 0, "0", 0, 0, 0, "1", 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "No - permittivity", "No - permittivity", "No - permittivity", "No - permittivity", "No - the subscript implies free space!", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Ueps0", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["V/m", "N/C", "C", "F/m", "none", "m", "J", "A", "V", "N", "F", "K", "eV", "Pa", "kg", "Hz"], "matrix": [0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Depsr", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", 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"variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["electric field strength", "electric flux", "charge", "point charge", "permeability", "permeability of free space", "permeability of the material", "relative permeability of the material", "permittivity of the material", "permittivity of free space", "relative permittivity of the material", "radius", "distance from the point charge", "displacement vector", "unit displacement vector", "unit&nbsp;radial vector"], "matrix": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "Of what?", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Ur", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["V/m", "N/C", "C", "F/m", "none", "m", "J", "A", "V", "N", "F", "K", "eV", "Pa", "kg", "Hz"], "matrix": [0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Drhat", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["electric field strength", "electric flux", "charge", "point charge", "permeability", "permeability of free space", "permeability of the material", "relative permeability of the material", "permittivity of the material", "permittivity of free space", "relative permittivity of the material", "radius", "distance from the point charge", "displacement vector", "unit displacement vector", "unit&nbsp;radial vector"], "matrix": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, "0", "1"], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Urhat", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["V/m", "N/C", "C", "F/m", "none", "m", "J", "A", "V", "N", "F", "K", "eV", "Pa", "kg", "Hz"], "matrix": [0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "E-field value", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the magnitude of the electric field {rmm}&nbsp;mm from a {q1mu}&nbsp;&mu;C point charge in vacuum.</p>\n<p style=\"text-align: center;\">$|\\vec{E}|=$ [[0]]&nbsp;[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "E value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "efield*0.995", "maxValue": "efield*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": true, "customName": "units", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["N/C", "V/m", "A/m", "J/m", "C/s", "F/m"], "matrix": ["1", "1", 0, 0, 0, 0], "distractors": ["", "", "", "", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Force", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the equation for the force that a second point charge, $q_2$ (q_2) would experience is placed in the electric field $E_1$ (E_1) due to the first point charge?</p>\n<p style=\"text-align: center;\">$F=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "q_2 E_1", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "e_1", "value": ""}, {"name": "q_2", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Force value", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "efield", "part": "p2g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the magnitude of the&nbsp;force a {q2mu}&nbsp;&mu;C point charge would experience if placed {rmm}&nbsp;mm from a {q1mu}&nbsp;&mu;C point charge in vacuum.</p>\n<p style=\"text-align: center;\">$|\\vec{F}|=$ [[0]]&nbsp;[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "F Value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "efield", "part": "p2g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "force*0.995", "maxValue": "force*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": true, "customName": "units", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["N", "V", "A", "J", "C", "F"], "matrix": ["1", "0", 0, 0, 0, 0], "distractors": ["", "", "", "", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Direction", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What are the directions of the forces experienced by both charges in this case (the direction for the vector with a positive magnitude)?</p>\n<p>[[0]]</p>", "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "Direction", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "4", "showCellAnswerState": true, "choices": ["<img src=\"resources/question-resources/CoulombForce1.png\"/>", "<img src=\"resources/question-resources/CoulombForce2.png\"/>", "<img src=\"resources/question-resources/CoulombForce3.png\"/>", "<img src=\"resources/question-resources/CoulombForce4.png\"/>"], "matrix": ["1", 0, 0, 0], "distractors": ["Opposite charges attract!", "Opposite charges attract!", "Opposite charges attract!", "Opposite charges attract!"]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Electric field from a point charge plus units", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Coulomb.svg", "/srv/numbas/media/question-resources/Coulomb.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}], "tags": ["coulomb", "elec", "field", "force", "tut1v", "units"], "metadata": {"description": "Simple numerical evaluation using a given formula.", "licence": "All rights reserved"}, "statement": "<p><img style=\"float: left;\" src=\"resources/question-resources/Coulomb.svg\"/> This question is about the electric field a distance from a point charge in vacuum.&nbsp;&nbsp;Coulomb's law states that the electric field from a point charge in vacuum is <br/> $\\displaystyle{q\\over4\\pi\\varepsilon_0r^2}$.<br/>When providing numerical answers you may express them using scientific notation.&nbsp; Express values to four significant figures and use the values of physical constants as provided in the course notes.</p>", "advice": "<p>You might have calculated the force on the second point charge using the full Coulomb force formula,</p>\n<p style=\"text-align: center;\">$\\displaystyle F={q_1q_2\\over4\\pi\\varepsilon r^2}$&nbsp;</p>\n<p>If you approached the question this way you have missed a functional use of the electric field as it provides directly the potential for a force to exist, so that $\\vec{F}=q\\vec{E}$.</p>\n<p>Common errors include unit slips and forgetting to square the distance.</p>", "rulesets": {}, "variables": {"r1": {"name": "r1", "group": "Ungrouped variables", "definition": "random(1..10#1)", "description": "<p>Random distance between 1 and 10 mm in steps of 1 mm (unit are mm)</p>", "templateType": "anything"}, "eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "8.854*10^-12", "description": "<p>Permitivitty of free space in F/m.</p>", "templateType": "anything"}, "Efield": {"name": "Efield", "group": "Ungrouped variables", "definition": "abs(q1n/(4*pi*eps0*r1n^2))", "description": "<p>Electric field strength in SI units for a point charge.</p>", "templateType": "anything"}, "q2n": {"name": "q2n", "group": "Ungrouped variables", "definition": "q2*10^(-9)", "description": "<p>q2 in C.</p>", "templateType": "anything"}, "q1": {"name": "q1", "group": "Ungrouped variables", "definition": "random(1..10#1)*random(-1..1#2)", "description": "<p>Random (point) charge between -10 and +10 nC.</p>", "templateType": "anything"}, "force": {"name": "force", "group": "Ungrouped variables", "definition": "abs(Efield*q2n)", "description": "<p>The force due to q1 experienced by q2 (N).</p>", "templateType": "anything"}, "q1n": {"name": "q1n", "group": "Ungrouped variables", "definition": "q1*10^-9", "description": "<p>q1 in C</p>", "templateType": "anything"}, "r1n": {"name": "r1n", "group": "Ungrouped variables", "definition": "r1/1000", "description": "<p>r1 in m</p>", "templateType": "anything"}, "q2": {"name": "q2", "group": "Ungrouped variables", "definition": "random(1..10#1 except abs(q1))*random(-1..1#2)", "description": "<p>The second point charge (nC).</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Efield", "eps0", "force", "q1", "q1n", "q2", "q2n", "r1", "r1n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Electric field", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate the magnitude of $E$ at a distance {r1}&nbsp;mm from a {q1}&nbsp;nC point-charge, and choose suitable units.</p>\n<p style=\"text-align: center;\">$|\\vec{E}|=$&nbsp;[[0]] [[1]].</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "E", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "Efield*0.995", "maxValue": "Efield*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": true, "customName": "units", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["V/m", "N/C", "m/V", "C/N", "V/C", "C/m", "N/m"], "matrix": ["1", "1", 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Force", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>A second point charge of magnitude {q2}&nbsp;nC is placed at the distance of {r1}&nbsp;mm from the original {q1}&nbsp;nC point charge.&nbsp; What is the magnitude of the force it will experience, and what are suitable units?</p>\n<p style=\"text-align: center;\">$|\\vec{F}|=$&nbsp;[[0]] [[1]].</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "force", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [{"variable": "Efield", "part": "p0g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "force*0.995", "maxValue": "force*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": true, "customName": "units", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["J/m", "J.m", "N.m", "N/m"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}], "type": "question"}, {"name": "Electrostatic potential and equipotentials", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}], "tags": ["coulomb", "elec", "potential", "tut1"], "metadata": {"description": "<p>The electrostatic potential due to a point charge is calculated at three points, who of which are at the same distance but different directions.&nbsp; This relates to the idea that the equipoptentials of a point charge are spheres centred on the charge, so all points at the same distance are at the same potential.</p><p>This question requires unit conversion, numerical calculations and some critical evaluation.</p>", "licence": "All rights reserved"}, "statement": "<p>A point charge is placed at the origin of a Cartesian co-ordinate system, in vacuum.&nbsp; In this problem we shall use the standard boundary condition for the electrostatic potential from a point charge, i.e. $V(\\infty)=0\\,\\text{V}$.</p>\n<p>When providing numerical answers you may express them using scientific notation.&nbsp; Express values to four significant figures and use the values of physical constants as provided in the course notes.</p>", "advice": "<p>Quantiative errors may occur due to unit conversion errors.</p>\n<p>A common error is mis-remembering the Coulomb potential which is an inverse distance rule, and not an inverse-square (which is what we see for the electric field in Coulomb's Law).&nbsp; If you squared the distance, revise this section of the course.</p>\n<p>The correct formula for the electrostatic potential due to a point charge, taking the boudary condition that $V(\\infty)=0$, is&nbsp;</p>\n<p>$\\displaystyle V(r)=\\frac{q}{4\\pi\\varepsilon r}$</p>\n<p>where $r$ is the distance from the point charge.&nbsp; Note, the electrostatic potential is a scalar field - it does not have a direction.</p>\n<p>If you calculated the distance and potential at point $c$, then you may have not understood the symmetry of the system and the idea that a point charge has spherical equipotentials.&nbsp; Since the distance from the point charge to the points $a$ and $c$ are the same, so is the electrostatic potential.</p>\n<p>The potential difference between point $c$ and 'infinity' is obtainable directly from the definition of the potential difference, which is the energy per unit charge.&nbsp; Therefore the energy gained (they are both positive charges so therefore repel) is {q2}&times;10<sup>&minus;6</sup>&times;$V_c$.</p>", "rulesets": {}, "variables": {"const": {"name": "const", "group": "Ungrouped variables", "definition": "(10^(-4))/(4*pi*eps0)", "description": "<p>$1/4\\pi\\varepsilon_0$ and a factor of 10,000 to convert cm and microC to get V in SI units.</p>", "templateType": "anything"}, "Vb": {"name": "Vb", "group": "Ungrouped variables", "definition": "q1*const/sqrt(x1^2+x1^2)", "description": "<p>Electrostatic potential at (x1,x1) in V.</p>", "templateType": "anything"}, "q1": {"name": "q1", "group": "Ungrouped variables", "definition": "random(10..100#10)*1.0", "description": "<p>Randomised value of the charge at the origin in $mu$C.</p>", "templateType": "anything"}, "Va": {"name": "Va", "group": "Ungrouped variables", "definition": "q1*const/sqrt(x1^2+x2^2)", "description": "<p>Electrostatic potential at (x1,x2) in V.</p>", "templateType": "anything"}, "rc": {"name": "rc", "group": "Ungrouped variables", "definition": "ra", "description": "<p>Distance of point c from the charge in cm.</p>", "templateType": "anything"}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(5..20#1)*1.0", "description": "<p>First $x$-location in cm.</p>", "templateType": "anything"}, "Vc": {"name": "Vc", "group": "Ungrouped variables", "definition": "Va", "description": "<p>Electrostatic potential at (x2,x1) in V.</p>", "templateType": "anything"}, "eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "decimal(8.854*10^(-12))", "description": "<p>Permittivity of free space (F/m) to four significant figures.</p>", "templateType": "anything"}, "rb": {"name": "rb", "group": "Ungrouped variables", "definition": "sqrt(x1^2+x1^2)", "description": "<p>Distance of point b from the charge in cm.</p>", "templateType": "anything"}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(5..20#1 except x1)*1.0", "description": "<p>Second $x$-position in cm.</p>", "templateType": "anything"}, "ra": {"name": "ra", "group": "Ungrouped variables", "definition": "sqrt(x1^2+x2^2)", "description": "<p>Distance of point a from the charge in cm.</p>", "templateType": "anything"}, "work": {"name": "work", "group": "Ungrouped variables", "definition": "q2*Vc*10^-6", "description": "", "templateType": "anything"}, "q2": {"name": "q2", "group": "Ungrouped variables", "definition": "random(1..100 except q1)*1.0", "description": "<p>Primitive charge</p>", "templateType": "anything"}, "test": {"name": "test", "group": "Ungrouped variables", "definition": "dec(1.6*10^-1.0)*1000000", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["const", "eps0", "q1", "ra", "rb", "rc", "Va", "Vb", "Vc", "x1", "x2", "work", "q2", "test"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Potential at $a$", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the electrostitic potential at the point $a$, with co-ordinates $x=${x1} cm, $y=${x2} cm, $z=$0 cm for a point charge of {q1} $\\mu$C located at the origin?</p>\n<p style=\"text-align: center;\">$r_a=$ [[1]] cm.</p>\n<p style=\"text-align: center;\">$V(r_a)=$[[0]] Volts.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "V_a", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Va*0.995", "maxValue": "Va*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "r_a", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ra*0.995", "maxValue": "ra*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Potential at $b$", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the electrostitic potential at the point $b$, with co-ordinates $x=${x1} cm, $y=${x1} cm, $z=$0 cm for a point charge of {q1} $\\mu$C located at the origin?</p>\n<p style=\"text-align: center;\">$r_b=$&nbsp;[[1]]&nbsp;cm.</p>\n<p style=\"text-align: center;\">$V(r_b)=$[[0]]&nbsp;Volts.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "V_b", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Vb*0.995", "maxValue": "Vb*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "r_b", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "rb*0.95", "maxValue": "rb*1.05", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Potential at $c$", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the electrostitic potential at the point $c$, with co-ordinates $x=${x2} cm, $y=${x1} cm, $z=$0 cm for the point charge of {q1} $\\mu$C located at the origin?</p>\n<p style=\"text-align: center;\">$r_c=$&nbsp;[[1]]&nbsp;cm.</p>\n<p style=\"text-align: center;\">$V(r_c)=$[[0]]&nbsp;Volts.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "V_c", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Vc*0.995", "maxValue": "Vc*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "r_c", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "rc*0.995", "maxValue": "rc*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "1_n_2", "useCustomName": true, "customName": "Relationship of points", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Two of the three values of $V(r_a)$, $V(r_b)$ and $V(r_c)$ have the same value.&nbsp; This is because...</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["The points are in the same direction from the charge.", "The points are at the same distance from the charge.", "Random chance - there's no underlying reason.", "Conservation of energy", "Conservation of momentum", "The principle of superposition"], "matrix": [0, "1", 0, 0, 0, 0], "distractors": ["No - equipotenials of a point charge are spheres centred upon it.", "Yes - equipotenials of a point charge are spheres centred upon it.", "No - equipotenials of a point charge are spheres centred upon it.", "", "", ""]}, {"type": "gapfill", "useCustomName": true, "customName": "Energy", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A point charge of {q2} &mu;C point is initially placed at $c$.&nbsp; The repulsive force moves it far from the origin.&nbsp; Taking it's final position to be effectively infinitly far from the {q1} &mu;C point charge at the origin, how much energy does this second charge gain in this process?</p>\n<p style=\"text-align: center;\">Energy gained = [[0]]&nbsp;J</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Energy", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "work*0.999", "maxValue": "work*1.001", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Electrostatic potential energy", "extensions": [], "custom_part_types": [], "resources": [["question-resources/DipoleArrangement_kjXrTbK.png", "/srv/numbas/media/question-resources/DipoleArrangement_kjXrTbK.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}], "tags": [], "metadata": {"description": "Determining a charge from the work done in moving an electron between two points in the field of the point charge.", "licence": "All rights reserved"}, "statement": "<p>When providing numerical answers you may express them using scientific notation.&nbsp; Express values to four significant figures and use the values of physical constants as provided in the course notes.</p>\n<p align=\"center\"><img width=\"250px\" align=\"center\" src=\"resources/question-resources/DipoleArrangement_kjXrTbK.png\"/></p>\n<p>A point-charge is located at a point P in vacuum as shown on the schematic, indicative diagram (axes and points not to scale).</p>", "advice": "<p>The electrostatic potential from a point charge is stated in the question.&nbsp; We have to take care in defining the meaning of the symbols and in using consistent units.&nbsp; In the question the \"normal\" units are not given as options, but in all cases the correct units can be derived from one or more of the options provided.&nbsp; For example, since 1A=1C/s, Coulombs are equivalent to Amp.seconds, and A.s/C is a dimensionless object (the units cancel).&nbsp;&nbsp;</p>\n<p>For the potential due to a point charge, we can determine the potential difference between the two points, A and B, due to a charge $q_1$ at P as</p>\n<p style=\"text-align: center;\">$\\displaystyle \\Delta V={q_1\\over4\\pi\\varepsilon}\\left({1\\over|\\vec{PA}|}-{1\\over|\\vec{PB}|}\\right)$,</p>\n<p>where $\\vec{PA}$ is the vector from P to A and&nbsp;$\\vec{PB}$ is the vector from P to B.</p>\n<p>We do not know the value of $q_1$ -- this is to be found -- but we do know the energy change in moving an electron (with a charge of $-1.6\\times 10^{-19}$C) from A to B.&nbsp; This is related to the potential difference simply as $-e\\Delta V$. (Checking units, the p.d. is in Volt=J/C so multiplication by a charge yeilds an energy.) We're told the energy difference in eV, so we need to know how to convert between eV and Joules: 1 eV=$e$ J.</p>\n<p>So to obtain the charge at P, we need to solve</p>\n<p style=\"text-align: center;\">$\\displaystyle \\Delta \\text{P.E.}=-e\\Delta V=-{eq_1\\over4\\pi\\varepsilon}\\left({1\\over|\\vec{PA}|}-{1\\over|\\vec{PB}|}\\right)$</p>\n<p>for $q_1$ (it's the only unknown).</p>\n<p>If the charge at P is positive, then it will cost energy to move an electron from A to B, whereas if the charge at P is negative, we will gain energy in the move so the cost will be negative.</p>", "rulesets": {}, "variables": {"eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "8.854*10^-12", "description": "<p>Permittivity of space in F/m.</p>", "templateType": "anything"}, "xa": {"name": "xa", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything"}, "xb": {"name": "xb", "group": "Ungrouped variables", "definition": "-xa", "description": "", "templateType": "anything"}, "xp": {"name": "xp", "group": "Ungrouped variables", "definition": "xa", "description": "", "templateType": "anything"}, "ya": {"name": "ya", "group": "Ungrouped variables", "definition": "random(-10..10)", "description": "", "templateType": "anything"}, "yb": {"name": "yb", "group": "Ungrouped variables", "definition": "ya", "description": "", "templateType": "anything"}, "yp": {"name": "yp", "group": "Ungrouped variables", "definition": "ya+random(5..10)", "description": "", "templateType": "anything"}, "q1n": {"name": "q1n", "group": "Ungrouped variables", "definition": "random(1..10)*random(-1..1#2)", "description": "", "templateType": "anything"}, "q1": {"name": "q1", "group": "Ungrouped variables", "definition": "q1n*10^-9", "description": "", "templateType": "anything"}, "ra": {"name": "ra", "group": "Ungrouped variables", "definition": "abs(yp-ya)/100", "description": "<p>In metres.</p>", "templateType": "anything"}, "rb": {"name": "rb", "group": "Ungrouped variables", "definition": "sqrt((xb-xp)^2+(yb-yp)^2)/100", "description": "<p>In metres.</p>", "templateType": "anything"}, "va": {"name": "va", "group": "Ungrouped variables", "definition": "q1/4/pi/eps0/ra", "description": "", "templateType": "anything"}, "vb": {"name": "vb", "group": "Ungrouped variables", "definition": "q1/4/pi/eps0/rb", "description": "", "templateType": "anything"}, "work": {"name": "work", "group": "Ungrouped variables", "definition": "pd*qe", "description": "", "templateType": "anything"}, "qe": {"name": "qe", "group": "Ungrouped variables", "definition": "-1.6*10^-19", "description": "", "templateType": "anything"}, "pd": {"name": "pd", "group": "Ungrouped variables", "definition": "vb-va", "description": "", "templateType": "anything"}, "workev": {"name": "workev", "group": "Ungrouped variables", "definition": "-work/qe", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["eps0", "pd", "q1", "q1n", "qe", "ra", "rb", "va", "vb", "work", "xa", "xb", "xp", "ya", "yb", "yp", "workev"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Potential formula", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The formula for the electrostatic potential is</p>\n<p style=\"text-align: center;\">$\\displaystyle V={q\\over4\\pi\\varepsilon r}$.&nbsp;</p>\n<p>Match the symbols to their descriptions.&nbsp; Some descriptions will be marked as partially correct (1 mark) but in all cases there is at least one option for full marks (2 marks).&nbsp; Only one option per symbol is allowed.</p>\n<p style=\"text-align: center;\">[[0]]</p>", "gaps": [{"type": "m_n_x", "useCustomName": true, "customName": "symbols and descriptions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "choices": ["$q$", "$r$", "$\\varepsilon$"], "matrix": [["2", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, "1", 0], [0, 0, 0, 0, 0, 0, 0, 0, "1", 0, "2", 0, 0], [0, 0, 0, 0, 0, 0, "2", 0, 0, 0, 0, 0, 0]], "layout": {"type": "all", "expression": ""}, "answers": ["magnitude of the point charge", "permittivity of free space", "permeability of free space", "relative permeability", "relative permittivity", "permeability", "permittivity", "radius", "distance", "radius of charge", "distance from charge", "charge", "radius of field"]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Units for quantities", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Match the units with the quantities.&nbsp; There may be more than one correct option for each case.</p>\n<p style=\"text-align: center;\">$q$: [[0]]</p>\n<p style=\"text-align: center;\">$r$:&nbsp;[[1]]</p>\n<p style=\"text-align: center;\">$\\varepsilon_0$:&nbsp;[[2]]</p>\n<p style=\"text-align: center;\">$\\varepsilon_r$:&nbsp;[[3]]</p>", "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "Charge", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["V", "A", "F", "m", "J", "F.V", "F/m", "A.s", "C/(V.m)", "nm", "J/N", "no units"], "matrix": [0, 0, 0, 0, 0, "1", 0, "1", 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "r", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["V", "A", "F", "C", "J", "F.V", "F/m", "A.s", "C/(V.m)", "J/N", "no units"], "matrix": [0, 0, 0, 0, 0, 0, 0, 0, 0, "1", 0], "distractors": ["", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "epsilon 1", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["V", "A", "F", "m", "C", "J", "F.V", "A.s", "C/(V.m)", "nm", "J/N", "no units"], "matrix": [0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "epsilon 2", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["V", "A", "F", "m", "C", "J", "F.V", "F/m", "A.s", "C/(V.m)", "nm", "J/N", "A.s/C"], "matrix": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, "2"], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Potential difference", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If the point charge at P is $q_1$ (q_1) and the distances from P to A and B are $r_a$ (r_a) and $r_b$ (r_b), respectively, what is the formula for the potential difference between A and B in terms of these variables and $\\varepsilon$ (epsilon)?</p>\n<p style=\"text-align: center;\">$V(r_a)-V(r_b)=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "formula", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "q_1 /4/pi/epsilon/r_a-q_1/4/pi/epsilon/r_b", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "epsilon", "value": ""}, {"name": "q_1", "value": ""}, {"name": "r_a", "value": ""}, {"name": "r_b", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Energy", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Charge $q_1$ is located at point P in the diagram.&nbsp; If a charge $q_2$ (q_2) is moved from point A to point B in the field due to $q_1$, what is the formula for the energy change in terms of the potential difference between A and B , $V$, and the charge $q_2$?</p>\n<p style=\"text-align: center;\">Change in energy$=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "q_2 V", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "q_2", "value": ""}, {"name": "v", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Charge at P", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A, B and P are the points ({xa}, {ya}), ({xb}, {yb}) and ({xp}, {yp}), with co-ordinates in units of cm.&nbsp; If the energy required to move an electron from A to B is {siground(workev,4)}&nbsp;eV, how much charge lies at the point P?&nbsp; Take care to correctly determine the sign of the charge as well as its magnitude.</p>\n<p style=\"text-align: center;\">Charge at P is&nbsp;[[0]] nC.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Q", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "q1n*0.999", "maxValue": "q1n*1.001", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Parallel-plate capacitor characteristics practice", "extensions": [], "custom_part_types": [], "resources": [["question-resources/PPC_wVHgAAr.png", "/srv/numbas/media/question-resources/PPC_wVHgAAr.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}], "tags": ["elec", "energy", "field", "mid1718", "PPC"], "metadata": {"description": "Mathematical relationships and their evaluation for parallel plate capacitors.", "licence": "All rights reserved"}, "statement": "<p><img style=\"float: left; width: 300px;\" src=\"resources/question-resources/PPC_wVHgAAr.png\"/> A capacitor is constructed from circular plates of diameter {diametermm}&nbsp;mm separated by a layer of electrically insulating material with a uniform thickness of {wmu}&nbsp;&mu;m. When a potential difference of {pdmv}&nbsp;mV is applied, charges of &minus;{qn}&nbsp;nC and {qn}&nbsp;nC are stored on the two plates.<br/> When providing numerical answers you may express them using scientific notation.&nbsp; Express values to four significant figures and use the values of physical constants as provided in the course notes.</p>", "advice": "<p>The equations required to anwer this question are:</p>\n<p style=\"text-align: center;\">$\\displaystyle C={Q\\over V}={\\varepsilon A\\over d}$</p>\n<p style=\"text-align: center;\">$\\displaystyle E={V\\over d}={\\sigma \\over \\varepsilon}$</p>\n<p style=\"text-align: center;\">$\\displaystyle \\sigma = {Q\\over A}$</p>\n<p style=\"text-align: left;\">and</p>\n<p style=\"text-align: center;\">Stored energy $\\displaystyle = {1\\over 2}QV$</p>\n<p style=\"text-align: left;\">where $C$ is the capacitance, $V$ is the potential difference between the plates, $A$ is the plate area, $d$ is the plate separation, $sigma$ is the charge density on a plate, $Q$ is the total charge on a plate and $\\varepsilon=\\varepsilon_0\\varepsilon_r$ is the permittivity of the material between the plates.&nbsp;</p>\n<p style=\"text-align: left;\">The formula for the electric field in terms of the charge density and the permittivity is derived from the application of Gauss' Law to an infinite sheet of uniform charge density, so is only an approximation.&nbsp; It is pretty accurate between the plates away from the edge if the gap is small compared to the length-scale of the plate.&nbsp; At the edge of the PPC the field is dipolar (not uniform).&nbsp; If the plates are far apart compared to the diameter of the plate, then the approximation is poor.</p>\n<p style=\"text-align: left;\">Finally, there are requirements to convert between units, so if you got the right numbers except for where the decimal point is, then check your unit conversion.&nbsp;</p>", "rulesets": {}, "variables": {"den": {"name": "den", "group": "Ungrouped variables", "definition": "deltaenergy*10^9", "description": "<p>Increase in energy, nJ.</p>", "templateType": "anything"}, "energy1": {"name": "energy1", "group": "Ungrouped variables", "definition": "0.5*q*pd", "description": "<p>Energy stored initially, J.</p>", "templateType": "anything"}, "emax": {"name": "emax", "group": "Ungrouped variables", "definition": "siground(efield,4)*random(2..5)", "description": "<p>maximum E-field (breakdown), V/m.</p>", "templateType": "anything"}, "eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "8.854*10^-12", "description": "<p>Permittivity of free space in F/m.</p>", "templateType": "anything"}, "deltaenergy": {"name": "deltaenergy", "group": "Ungrouped variables", "definition": "energymax-energy1", "description": "<p>Energy required to increase the charge to the max, J.</p>", "templateType": "anything"}, "pd": {"name": "pd", "group": "Ungrouped variables", "definition": "pdmv/1000", "description": "<p>Potential difference in V.</p>", "templateType": "anything"}, "qn": {"name": "qn", "group": "Ungrouped variables", "definition": "random(1..10)*0.1", "description": "<p>Charge on each plate in nC.</p>", "templateType": "anything"}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "wmu*10^-6", "description": "<p>Separation of plates in m.</p>", "templateType": "anything"}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "qn*10^-9", "description": "<p>Charge in Coulombs.</p>", "templateType": "anything"}, "energymax": {"name": "energymax", "group": "Ungrouped variables", "definition": "0.5*qmax*emax*w", "description": "<p>Max energy stored, J.</p>", "templateType": "anything"}, "area": {"name": "area", "group": "Ungrouped variables", "definition": "pi*(diameter/2)^2", "description": "<p>Plate area in m^2.</p>", "templateType": "anything"}, "diametermm": {"name": "diametermm", "group": "Ungrouped variables", "definition": "random(2..5#0.5)", "description": "<p>Diameter of plates in mm.</p>", "templateType": "anything"}, "qmax": {"name": "qmax", "group": "Ungrouped variables", "definition": "capacitance * emax * w", "description": "<p>Maximum stored charge, C.</p>", "templateType": "anything"}, "wmu": {"name": "wmu", "group": "Ungrouped variables", "definition": "random(6..20#2)", "description": "<p>Separation of plates in um.</p>", "templateType": "anything"}, "pdmv": {"name": "pdmv", "group": "Ungrouped variables", "definition": "random(100..500#100)", "description": "<p>Potential difference in mV</p>", "templateType": "anything"}, "diameter": {"name": "diameter", "group": "Ungrouped variables", "definition": "diametermm/1000", "description": "<p>Diameter in m</p>", "templateType": "anything"}, "sigma": {"name": "sigma", "group": "Ungrouped variables", "definition": "q/area", "description": "<p>Charge density in C/m^2.</p>", "templateType": "anything"}, "epsr": {"name": "epsr", "group": "Ungrouped variables", "definition": "Q w / (pd * area *eps0)", "description": "<p>Relative permittivity.</p>", "templateType": "anything"}, "capacitance": {"name": "capacitance", "group": "Ungrouped variables", "definition": "q/pd", "description": "<p>Capacitance in F.</p>", "templateType": "anything"}, "efield": {"name": "efield", "group": "Ungrouped variables", "definition": "pd/w", "description": "<p>Electric field in V/m.</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["area", "capacitance", "deltaenergy", "den", "diameter", "diametermm", "efield", "emax", "energy1", "energymax", "eps0", "epsr", "pd", "pdmv", "q", "qmax", "qn", "sigma", "w", "wmu"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Electric field strength", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the formula for the electric field strength in terms of the potential difference, $V$, and the separation of the plates, $d$?</p>\n<p style=\"text-align: center;\">$|\\vec{E}|=$&nbsp;[[1]]</p>\n<p>Calculate the magnitude of the electric field.</p>\n<p style=\"text-align: center;\">$|\\vec{E}|=$&nbsp;[[0]] V/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "efield", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "efield*0.995", "maxValue": "efield*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": true, "customName": "Formula", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "V/d", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "valuegenerators": [{"name": "d", "value": ""}, {"name": "v", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "The charge density", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the formula for the&nbsp;charge density&nbsp;in terms of the charge, $Q$, and the&nbsp;radius of the plate, $r$.</p>\n<p style=\"text-align: center;\">$\\sigma=$&nbsp;[[1]]</p>\n<p>Calculate the charge density on the positive plate.</p>\n<p style=\"text-align: center;\">$\\sigma=$&nbsp;[[0]]&nbsp;C.m$^{-2}$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "sigma", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "sigma*0.995", "maxValue": "sigma*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": true, "customName": "formula", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "Q/(pi r^2)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "valuegenerators": [{"name": "q", "value": ""}, {"name": "r", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Capacitance", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the formula for the capacitance&nbsp;in terms of the charge, $Q$, and the potential difference, $V$.</p>\n<p style=\"text-align: center;\">$C=$&nbsp;[[1]]</p>\n<p>Calculate the capacitance.</p>\n<p style=\"text-align: center;\">$C=$&nbsp;[[0]]&nbsp;Farads</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Capacitance", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "capacitance*0.995", "maxValue": "capacitance*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": true, "customName": "formula", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "Q/V", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "valuegenerators": [{"name": "q", "value": ""}, {"name": "v", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Relative permittivity", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the formula for the&nbsp;relative permittivity in terms of the charge, $Q$, the separation of the plates, $d$, the potential difference, $V$, the plate area, $A$ and the permittivity of free space, $\\varepsilon_0$ (epsilon_0).</p>\n<p style=\"text-align: center;\">$\\varepsilon_r=$&nbsp;[[1]]</p>\n<p>Calculate the value of the relative permittivity.</p>\n<p style=\"text-align: center;\">$\\varepsilon_r=$&nbsp;[[0]]&nbsp;</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Epsilon", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "epsr*0.995", "maxValue": "epsr*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": true, "customName": "formula", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "Q D/(V A epsilon_0)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "valuegenerators": [{"name": "a", "value": ""}, {"name": "d", "value": ""}, {"name": "epsilon_0", "value": ""}, {"name": "q", "value": ""}, {"name": "v", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Maximum charge", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The insulating material between the plates will fail (start to conduct electricity) if the magnitude of the electric field strength exceeds {emax} N/C.&nbsp; What is the maximum charge that can be stored?</p>\n<p style=\"text-align: center;\">$Q_{\\rm max}=$&nbsp;[[0]]&nbsp;Coulombs</p>\n<p style=\"text-align: left;\">How much energy is required to increase the charge from {qn} nC to this maximum value?</p>\n<p style=\"text-align: center;\">Increase in energy =&nbsp;[[1]]&nbsp;nano-Joules.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Max charge", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [{"variable": "epsr", "part": "p3g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "qmax*0.995", "maxValue": "qmax*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Energy", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "den*0.995", "maxValue": "den*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "m_n_x", "useCustomName": true, "customName": "Match the ideas", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Match the parts that are true for the PPC in the question.&nbsp; Note, there may be more than one acceptable answer.&nbsp; You will get a mark deducted for each incorrect answer.</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": true, "displayType": "checkbox", "warningType": "none", "showCellAnswerState": true, "choices": ["The field as $E=\\sigma/\\varepsilon$ is best approximated", "The field is dipolar", "The electric field points", "The field as $E=\\sigma/\\varepsilon$ is a poor approximation"], "matrix": [["1", "-1", "1", "-1", "-1", "-1"], ["-1", "1", "-1", "-1", "-1", "1"], ["-1", "-1", "-1", "1", 0, "-1"], ["-1", "1", "-1", "-1", "-1", "1"]], "layout": {"type": "all", "expression": ""}, "answers": ["in the middle of the capacitor", "at the edge of the capacitor", "if the diameter is much bigger than the separation", "from positive to negative", "from negative to positive", "if the diameter is&nbsp;similar to or smaller&nbsp;than the separation"]}], "type": "question"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, 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