// Numbas version: finer_feedback_settings
{"name": "Gauss' Law", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Gauss' Law", "tags": ["elec", "field", "flux", "gauss", "Gauss"], "metadata": {"description": "Questions relating to the principles of application of Gauss' Law to simple systems.", "licence": "All rights reserved"}, "statement": "<p>Gauss' Law is a powerful, general expression that links the arrangement of charges to the electric field strength, $\\vec{E}$.&nbsp;&nbsp;The mathematical formulation of the Law links the electric field flux through a closed surface, $\\phi_{\\rm electric}$ to the charge contained within that surface, $q$.</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>This is partly a mathematical and partly a computational problem, but it centres upon the formulation of Gauss' Law as&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle \\phi_{\\rm electric}=\\oint_S \\vec{E}.d\\vec{A}={q\\over\\varepsilon}$,</p>\n<p>where $\\phi_{\\rm electric}$ is the electric field flux through the closed Gaussian surface, $S$,&nbsp;$\\vec{E}$ is the electric field through $S$, $d\\vec{A}$ is an element of the surface area, $q$ is the total charge containined within $S$ and $\\varepsilon$ is the permittivity.&nbsp;&nbsp;</p>\n<p>To address the numerical part, we simply note that the arrangement of the charge is not relevant (Gauss' law applies whatever the arrangement of the charge within the closed surface) and so we can use&nbsp;&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle |\\phi_{\\rm electric}|=\\left|{q\\over\\varepsilon}\\right|=\\left|{e N_{\\rm electron}\\over\\varepsilon}\\right|$,</p>\n<p style=\"text-align: left;\">where $e=1.6\\times10^{-19}$C is the primitive charge.</p>", "rulesets": {}, "extensions": [], "variables": {"flux": {"name": "flux", "group": "Ungrouped variables", "definition": "nelec*qe/eps0", "description": "<p>flux in V.m</p>", "templateType": "anything"}, "chargee": {"name": "chargee", "group": "Ungrouped variables", "definition": "charge/qe", "description": "<p>Number of electrons within the Gaussian surface.</p>", "templateType": "anything"}, "eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "decimal(8.854*10^(-12))", "description": "<p>Permittivity of free space, F/m</p>", "templateType": "anything"}, "qe": {"name": "qe", "group": "Ungrouped variables", "definition": "decimal(1.6*10^-19)", "description": "<p>Charge on an electron, C.</p>", "templateType": "anything"}, "nelec": {"name": "nelec", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "<p>Number of electrons inside the Gaussian surface.</p>", "templateType": "anything"}, "charge": {"name": "charge", "group": "Ungrouped variables", "definition": "flux * eps0", "description": "<p>Charge contained within the Gaussian surface in C.</p>", "templateType": "anything"}, "fluxnm": {"name": "fluxnm", "group": "Ungrouped variables", "definition": "siground(flux*10^9,4)", "description": "<p>Flux through Gaussian surface in V.nm</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["charge", "chargee", "eps0", "flux", "fluxnm", "qe", "nelec"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Flux through the surface", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The flux through the surface expressed as an integral in terms of the electric field strength $\\vec{E}$ (NUMBAS input Efield) and the elements of the surface, $d\\vec{A}$ (NUMBAS input dA) is an integral over the closed surface, $S$, expressed as&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle \\phi=\\oint_S$[[0]]</p>\n<p style=\"text-align: left;\">Your answer should be input as either a dot prodct using 'dot(a,b)' where a and b are the symbols for the vectors, or a cross product using 'cross(a,b)'.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Flux through the surface", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "dot(Efield,dA)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "da", "value": ""}, {"name": "efield", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Charge term", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The flux through the surface is equal to a quantity depending upon the charge contained within the surface, $q$, and the permittivity of the space containing the charge, $\\varepsilon$ (NUMBAS input epsilon).&nbsp; This quantity is</p>\n<p style=\"text-align: center;\">[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Charge term", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "q/epsilon", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "epsilon", "value": ""}, {"name": "q", "value": ""}]}], "sortAnswers": false}, {"type": "m_n_2", "useCustomName": true, "customName": "Choice of Gaussian Surface", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>When selecting a&nbsp;<strong>Gaussian surface</strong> one might take a number of factors into account.&nbsp; Indicate at least 1 typical condition.&nbsp; Note well - marks are deducted for inappropriate answers.</p>", "minMarks": "-100", "maxMarks": "2", "shuffleChoices": true, "displayType": "checkbox", "displayColumns": "2", "minAnswers": "1", "maxAnswers": 0, "warningType": "prevent", "showCellAnswerState": true, "choices": ["The symmetry of the system.", "Make the volume contained by the surface as big as possible.", "Make the volume contained by the surface as small as possible.", "The surface must be a sphere.", "Must have plane surfaces (e.g. a cube)", "It helps for&nbsp;the flux to pass through the surface parallel to the surface normal.", "There's always a 'correct' answer to the choice of Gaussian surface, we just need to work it out."], "matrix": ["1", "-1", 0, "-1", "-1", "1", "-1"], "distractors": ["We need to make the integral integrable!", "The volume is usually irrelevant.", "The volume is usually irrelevant.", "Only applies to the analytical solution for a point or spherical charge arrangement.", "Generally not the case.", "This is generally useful as it makes the integration straight forward.", "The formulation of Gauss' Law is general and not unique to a specific surface - we're just after something we can do the maths for..."]}, {"type": "gapfill", "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, "prompt": "<p>The electric field from an arrangement of charge is found to give rise to an electric flux through a Gaussian surface of {fluxnm} volt-nanometres.&nbsp; &nbsp;If the charge is otherwise in vacuum, what is the total amount of charge inside the Gaussian surface?</p>\n<p style=\"text-align: center;\">$|Q|=$&nbsp;[[0]] Coulombs</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Charge", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "charge*0.995", "maxValue": "charge*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": "Number of electrons", "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 charge in the previous question is due to a collection of electrons, how many are inside the Gaussian surface?</p>\n<p style=\"text-align: center;\">$n_{\\rm electrons}=$&nbsp;[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "N", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "nelec", "maxValue": "nelec", "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", "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/"}]}