// Numbas version: finer_feedback_settings
{"name": "Field in the centre of of a wire loop", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Picture_1_KeCQXYx.png", "/srv/numbas/media/question-resources/Picture_1_KeCQXYx.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Field in the centre of of a wire loop", "tags": ["mag"], "metadata": {"description": "<p>Field and force (no prior knowledge required for the force)</p>", "licence": "All rights reserved"}, "statement": "<p>Consider a single loop of wire carring a constant current.&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 field at the centre of a circular current loop has a magnitude $H=j/2R$, where $j$ is the current and $R$ is the radius of the loop.&nbsp; The direction can be found using the right-hand screw rule: grab the wire with your right hand so that the thumb points along the direction of the current.&nbsp; The field circulates around the wire in the direction that your fingers are pointing.</p>\n<p>The expression for the force provided in the question is the magnetic term in the Lorentz force.&nbsp; You're told that it's an electron moving which means $q=-1.6\\times10^{-19}$C, and the formula for $B$ is what's required for the preceding step, i.e.&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle |\\vec{B}|=\\mu_0|\\vec{H}|={\\mu_0j \\over 2R}\\Rightarrow|\\vec{F}|={eu\\mu_0j \\over 2R}$</p>\n<p>There are no unknowns on the right hand side so a value for the force can be determined.&nbsp; The force of {forcef} fN determined in this case seems rediculously small and essentially zero, but we have to note that the electron also has a very small mass (order $10^{-30}$kg), so it will result in a very high acceleration!</p>", "rulesets": {}, "extensions": [], "variables": {"radiuscm": {"name": "radiuscm", "group": "Ungrouped variables", "definition": "random(1..5#0.1)", "description": "", "templateType": "anything"}, "radius": {"name": "radius", "group": "Ungrouped variables", "definition": "radiuscm*0.01", "description": "", "templateType": "anything"}, "speed": {"name": "speed", "group": "Ungrouped variables", "definition": "random(1..10#0.01)*10^7", "description": "", "templateType": "anything"}, "current": {"name": "current", "group": "Ungrouped variables", "definition": "random(0..2#0.01)+2", "description": "", "templateType": "anything"}, "hfield": {"name": "hfield", "group": "Ungrouped variables", "definition": "current*0.5/radius", "description": "", "templateType": "anything"}, "mu": {"name": "mu", "group": "Ungrouped variables", "definition": "4*10^-7*pi", "description": "", "templateType": "anything"}, "bfield": {"name": "bfield", "group": "Ungrouped variables", "definition": "mu*hfield", "description": "", "templateType": "anything"}, "force": {"name": "force", "group": "Ungrouped variables", "definition": "abs(decimal(speed*bfield*q))", "description": "<p>Force on the electron in fM</p>", "templateType": "anything"}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "decimal(-1.6*10^-4)", "description": "<p>Charge on an electron in fC</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["radiuscm", "radius", "speed", "current", "hfield", "mu", "bfield", "force", "q"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": true, "customName": "Field from a circular current", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of the following relative orientations of a current and the magnetic flux density its generated are consistent?</p>\n<p><img src=\"resources/question-resources/Picture_1_KeCQXYx.png\" alt=\"Image showing current and field in different relative directions\"/></p>\n<p></p>", "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": "4", "minAnswers": "1", "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["A", "B", "C", "D"], "matrix": ["1", "-1", "-1", "1"], "distractors": ["", "", "", ""]}, {"type": "gapfill", "useCustomName": true, "customName": "Formula", "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 magnitude of the magnetic flux density at the centre of the loop?&nbsp; Express your answer in terms of the radius of the loop, $R$, the current in the wire, $j$, and the permeability of free space $\\mu_0$ (mu_0).</p>\n<p style=\"text-align: center;\">$|B|=$[[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": "mu_0 j/(2R)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "j", "value": ""}, {"name": "mu_0", "value": ""}, {"name": "r", "value": ""}]}], "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>The magnitude of the force on a moving charge at the centre of the loop is&nbsp;</p>\n<p style=\"text-align: center;\">$|\\vec{F}|=|qu\\vec{B}|$</p>\n<p style=\"text-align: left;\">where $q$ is the amount of charge, and $u$ is the speed it is moving (the component of the velocity in the plane of the loop).</p>\n<p style=\"text-align: left;\">If an electron is moving with $u=${speed}&nbsp;m/s, $j=${current}&nbsp;A and the radius of the loop is $R=${radiuscm}&nbsp;cm, what is the force the electron experiences?</p>\n<p style=\"text-align: center;\">$|F|=$[[0]]&nbsp;femto-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*0.99", "maxValue": "force*1.01", "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/"}]}