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{"name": "Fields from bundles of wires", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Fields from bundles of wires", "tags": [], "metadata": {"description": "<p>Combination of fields from a bundle of wires.</p>", "licence": "All rights reserved"}, "statement": "<p>A tightly packed bundle of electrically insulated long, straight, parallel wires are connected together at their ends, and then plugged into a power source, so that an electrical current flows.&nbsp; 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 a question that draws upon the ideas of the field from a long straight wire, and from the notions of current and voltage.&nbsp; The bundle of wires can be thought of as a single current, but we have to be careful about determining how much current we have passing through the wires.</p>\n<p>First, we note that if there is a current $j_1$ in each wire, the total current is $Nj_1$, where $N$ is the number of wires.&nbsp; The field is then&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle \\left|\\vec{H}\\right|={j\\over 2\\pi R}$</p>\n<p>In the first instance we have a constant potential difference across the bundle.&nbsp; Each wire has the same potential difference (voltage) so that by Ohms-law we can determine the current in one wire to be&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle j_1={V\\over R_1}$</p>\n<p>where $R_1$ is the resistance of a single wire.&nbsp; We could determine the total resistance of the bundle to be $R_1/N$, since they are in parallel.&nbsp; Alternatively we could note that the same current, $j_1$, is flowing through each wire, so the total current is the sum of the currents over all the wires.&nbsp; Either way&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle j={NV \\over R_1}$</p>\n<p>For the second case we have a constant current source attached to the wires.&nbsp; This specifies the current all the wires together, so that in this case the input current is split between the {nwires} wires, i.e.&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle j_1={j\\over N}$</p>\n<p>We're not really interested in $j_1$, so we simply use $j$ for the determination of the field.&nbsp;</p>\n<p>The assumptions we need to make is that the bundle of wires is tightly packed so that the distance we're determining the field further from the bundle that the overall cross-sectional area of the bundle.&nbsp;&nbsp;</p>", "rulesets": {}, "extensions": [], "variables": {"nwires": {"name": "nwires", "group": "Ungrouped variables", "definition": "random(10..100)", "description": "<p>Number of wires in the bundle</p>", "templateType": "anything"}, "mu": {"name": "mu", "group": "Ungrouped variables", "definition": "4*10^-7*pi", "description": "<p>Permeability of free space in Tm/A</p>", "templateType": "anything"}, "diametermm": {"name": "diametermm", "group": "Ungrouped variables", "definition": "random(0.1..1#0.1)", "description": "<p>Diameter of each wire in mm.</p>", "templateType": "anything"}, "distancecm": {"name": "distancecm", "group": "Ungrouped variables", "definition": "random(1..5#0.1)", "description": "<p>Distance from the (centre of) the bundle to the point at which the field is being determined.</p>", "templateType": "anything"}, "hpd": {"name": "hpd", "group": "Ungrouped variables", "definition": "currentv/2/pi/distance", "description": "", "templateType": "anything"}, "distance": {"name": "distance", "group": "Ungrouped variables", "definition": "distancecm*0.01", "description": "", "templateType": "anything"}, "current": {"name": "current", "group": "Ungrouped variables", "definition": "random(0.1..0.5#0.01)", "description": "", "templateType": "anything"}, "voltage": {"name": "voltage", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything"}, "currentv": {"name": "currentv", "group": "Ungrouped variables", "definition": "voltage*1.0/(resistance/nwires)", "description": "", "templateType": "anything"}, "resistance": {"name": "resistance", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "<p>Resistance of each wire in Ohms.</p>", "templateType": "anything"}, "hi": {"name": "hi", "group": "Ungrouped variables", "definition": "current/2/pi/distance", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["nwires", "mu", "diametermm", "distancecm", "hpd", "distance", "current", "voltage", "currentv", "resistance", "hi"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "H-field", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The wires are circular in cross-section and have a diameter of {diametermm}mm.&nbsp; There are {nwires} individual wires in the bundle, each of which has an electrical resistance of {resistance}&nbsp;&Omega;.</p>\n<p>Write down an expression for the magnetising field strength as a function of distance&nbsp;from the bundle. (You will have to make some assumptions.)&nbsp; Express your answer in terms of the current in each wire, $j$, the number of wires, $N$ and the distance of the bundle to the point at which the field is being determined, $R$.</p>\n<p style=\"text-align: center;\">$|H|=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "H formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "N j /(2 pi R)", "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": "n", "value": ""}, {"name": "r", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Voltage source", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The power source is initially set to a fixed voltage of {voltage}V.&nbsp; What is the magnitude of the magnetizing field strength {distancecm} cm from the wire bundle?</p>\n<p style=\"text-align: center;\">$|H|=$[[0]]&nbsp;A/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Hpd", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "hpd*0.99", "maxValue": "hpd*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "04", "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": "Current source", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The power source is next set to a&nbsp;current&nbsp;source&nbsp;of {current}A.&nbsp; What is the magnitude of the magnetizing field strength also at a distance of {distancecm} cm from the wire bundle in this revised case?</p>\n<p style=\"text-align: center;\">$|H|=$[[0]]&nbsp;A/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Hcurrent", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "hi*0.99", "maxValue": "hi*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "04", "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/"}]}