// Numbas version: exam_results_page_options
{"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Electrostatic potential energy", "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": {}, "extensions": [], "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", "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/"}]}