// Numbas version: exam_results_page_options
{"name": "Electric field from a point charge", "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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Electric field from a point charge", "tags": [], "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": {}, "extensions": [], "variables": {"force": {"name": "force", "group": "Ungrouped variables", "definition": "abs(Efield*q2n)", "description": "<p>The force due to q1 experienced by q2 (N).</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"}, "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"}, "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"}, "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"}, "eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "8.854*10^-12", "description": "<p>Permitivitty of free space in F/m.</p>", "templateType": "anything"}, "q2n": {"name": "q2n", "group": "Ungrouped variables", "definition": "q2*10^(-9)", "description": "<p>q2 in C.</p>", "templateType": "anything"}, "q1n": {"name": "q1n", "group": "Ungrouped variables", "definition": "q1*10^-9", "description": "<p>q1 in C</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, "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 $E$ at a distance {r1}&nbsp;mm from a {q1}&nbsp;nC point-charge.</p>\n<p style=\"text-align: center;\">$|\\vec{E}|=$&nbsp;[[0]]&nbsp;V/m.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "E", "marks": "2", "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"}], "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>A second point charge of magnitude {q2} nC is placed at the distance of {r1} mm from the original {q1} nC point charge.&nbsp; What is the magnitude of the force it will experience?</p>\n<p style=\"text-align: center;\">$|\\vec{F}|=$&nbsp;[[0]] Newtons.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "force", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "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"}], "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/"}]}