// Numbas version: exam_results_page_options
{"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Coulomb forces", "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": {}, "extensions": [], "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", "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}]}]}], "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}]}