// Numbas version: finer_feedback_settings
{"name": "E&M 9: Toroidal solenoid quiz", "metadata": {"description": "<p>Practice questions for the toroidal solenoid.</p>", "licence": "All rights reserved"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "questions": [{"name": "Characteristics of a toriodal solenoid", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}], "tags": ["energy", "field", "flux", "inductance", "mag", "reluctance", "solenoid", "tut2"], "metadata": {"description": "A series of calculations and formulae for the characteristics of a toriodal solenoid operating as an inductor.", "licence": "All rights reserved"}, "statement": "<p>A toriodal solenoid is constructed to act as an inductor.&nbsp; It has the following properties:</p>\n<ul>\n<li>{turns} turns of wire, $N$</li>\n<li>{rcore*100} cm core radius, $r$</li>\n<li>{rring*100} cm ring radius, $R$</li>\n<li>{mur} core relative permeability, $\\mu_r$ (mu_r)</li>\n<li>{current} A current in the coil, $i$</li>\n</ul>\n<p>When entering formulae use only the above symbols along with the symbol for permeability of free space, $\\mu_0$ (mu_0), the magnetic flux, $\\phi$ (phi), the magnetic flux density, $B$, the magnetising field strength, $H$, the flux linkage, $\\Psi$ (psi), the inductance, $L$, the reluctance, $S$, and the stored energy, $U$.&nbsp; In each case use the simplest formula based upon the quantity from the previous part.</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 question is an example of a series of linked quantities.&nbsp;</p>\n<p style=\"text-align: center;\">${\\rm MMF}= N i=${mmf} Amps</p>\n<p style=\"text-align: center;\">$|H|=\\displaystyle{{\\rm MMF}\\over {\\rm path~length}}=\\displaystyle{Ni\\over2\\pi R}=${Hfield} A/m</p>\n<p style=\"text-align: center;\">$|B|=\\mu_0\\mu_r|H|=\\mu|H|=${Bfield} T</p>\n<p style=\"text-align: center;\">$\\phi=B A=${phi} Wb</p>\n<p style=\"text-align: center;\">$\\Psi = N \\phi=${Psi} Wb</p>\n<p style=\"text-align: center;\">$L = \\displaystyle{\\Psi\\over i}=${inductance} Henrys</p>\n<p style=\"text-align: center;\">$\\text{Stored energy}={1\\over2}Li^2=${energy} Joules</p>\n<p style=\"text-align: left;\">The field that a given ferro-magnetic material can amplify is limited to its saturation value.&nbsp; Raising the current beyond this point does not increase the flux density beyond the base-line $\\mu_0$ level.&nbsp; If we know the saturation field, $B_{\\rm sat}$, then we can determine the current since we can re-arrange the formulae above to give</p>\n<p style=\"text-align: center;\">$B_{\\rm sat}=\\mu H=\\displaystyle{\\mu N i_{\\rm sat}\\over 2\\pi R}\\Rightarrow i_{\\rm sat}=\\displaystyle{2\\pi RB_{\\rm sat}\\over \\mu_0 \\mu_r N}=${isat} Amps</p>\n<p style=\"text-align: left;\">The flux-linkage rises up to the point of saturation, so a current increase beyond this point simply reduces the inductance (since $L=\\Psi_{\\rm sat}/i$).</p>", "rulesets": {}, "variables": {"mmf": {"name": "mmf", "group": "Ungrouped variables", "definition": "turns * current", "description": "<p>Calculated MMF, Amps.</p>", "templateType": "anything"}, "xsection": {"name": "xsection", "group": "Ungrouped variables", "definition": "pi * rcore^2", "description": "<p>Cross-sectional area of core (m^2).</p>", "templateType": "anything"}, "rcore": {"name": "rcore", "group": "Ungrouped variables", "definition": "random(0.01..0.02#0.01)", "description": "<p>Core radius in metres.</p>", "templateType": "anything"}, "rring": {"name": "rring", "group": "Ungrouped variables", "definition": "rcore+random(0.02..0.03#0.01)", "description": "<p>Ring radius in metres.</p>", "templateType": "anything"}, "Bfield": {"name": "Bfield", "group": "Ungrouped variables", "definition": "mur * mu0 * Hfield", "description": "", "templateType": "anything"}, "reluctance": {"name": "reluctance", "group": "Ungrouped variables", "definition": "turns^2/inductance", "description": "<p>Calculated inductance (H^-1)</p>", "templateType": "anything"}, "phi": {"name": "phi", "group": "Ungrouped variables", "definition": "Bfield*xsection", "description": "<p>Calculated flux (T).</p>", "templateType": "anything"}, "energy": {"name": "energy", "group": "Ungrouped variables", "definition": "0.5*inductance*current^2", "description": "<p>Calculated stored energy (J).</p>", "templateType": "anything"}, "turns": {"name": "turns", "group": "Ungrouped variables", "definition": "random(300..500#20)", "description": "<p>Number of turns in the solenoid.</p>", "templateType": "anything"}, "psi": {"name": "psi", "group": "Ungrouped variables", "definition": "turns * phi", "description": "<p>Flux linkage, Wb</p>", "templateType": "anything"}, "Bsat": {"name": "Bsat", "group": "Ungrouped variables", "definition": "Bfield+random(0.8..1.2#0.1)", "description": "<p>Flux density at which the ferrite core 'saturates' in Tesla.</p>", "templateType": "anything"}, "current": {"name": "current", "group": "Ungrouped variables", "definition": "random(0.5..1.5#0.1)", "description": "<p>Current in the coil (Amps)</p>", "templateType": "anything"}, "mu": {"name": "mu", "group": "Ungrouped variables", "definition": "mur * mu0", "description": "<p>Total permeability.</p>", "templateType": "anything"}, "mu0": {"name": "mu0", "group": "Ungrouped variables", "definition": "pi*4*10^(-7)", "description": "<p>Permeability of free space, H/m</p>", "templateType": "anything"}, "inductance": {"name": "inductance", "group": "Ungrouped variables", "definition": "psi/current", "description": "<p>Calculated inductance (Henry)</p>", "templateType": "anything"}, "mur": {"name": "mur", "group": "Ungrouped variables", "definition": "random(80..160#10)", "description": "<p>Relative permeability of the core.</p>", "templateType": "anything"}, "isat": {"name": "isat", "group": "Ungrouped variables", "definition": "Bsat * 2 * pi * rring/(mu *turns)", "description": "<p>Calculated current to achieve saturated B-field (Amps)</p>", "templateType": "anything"}, "Hfield": {"name": "Hfield", "group": "Ungrouped variables", "definition": "mmf / (2 pi rring)", "description": "<p>Calculated H-field, A/m.</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Bfield", "Bsat", "current", "energy", "Hfield", "inductance", "isat", "mmf", "mu", "mu0", "mur", "phi", "psi", "rcore", "reluctance", "rring", "turns", "xsection"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "MMF", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The mathematical expression for the MMF is ${\\rm MMF} =$[[0]].</p>\n<p>The value of the MMF is&nbsp;[[1]] Amps.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "MMF formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "N i", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "n", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "MMF value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "mmf*0.95", "maxValue": "mmf*1.05", "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": "Magnetising field strength", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The mathematical expression for the&nbsp;magnetising field strength in the core is $|H| =$[[0]].</p>\n<p>The value of $|H|$ is&nbsp;[[1]] Amps/m.</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 i / (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": "n", "value": ""}, {"name": "r", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "H value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Hfield*0.95", "maxValue": "Hfield*1.05", "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": "Magnetic flux density", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The mathematical expression for the magnetic flux density in the core is $|B| =$[[0]].</p>\n<p>The value of $|B|$ is&nbsp;[[1]]&nbsp;Tesla.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "B 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 mu_r H", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "h", "value": ""}, {"name": "mu_0", "value": ""}, {"name": "mu_r", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "B value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Bfield*0.95", "maxValue": "Bfield*1.05", "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": "Magnetic flux", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The mathematical expression for the magnetic flux in the core is $\\phi =$[[0]].</p>\n<p>The value of $\\phi$ is&nbsp;[[1]]&nbsp;Wb.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "$\\phi$ formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "B A", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "a", "value": ""}, {"name": "b", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "$\\phi$ value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "phi*0.95", "maxValue": "phi*1.05", "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": "Flux linkage", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The mathematical expression for the flux linkage with the coil is $\\Psi =$[[0]].</p>\n<p>The value of $\\Psi$ is&nbsp;[[1]]&nbsp;Wb.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "$\\Psi$ formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "phi N", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "n", "value": ""}, {"name": "phi", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "$\\Psi$ value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "psi*0.95", "maxValue": "psi*1.05", "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": "Inductance", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The mathematical expression for the solenoid inductance is $L =$[[0]].</p>\n<p>The value of $L$ is&nbsp;[[1]]&nbsp;Henrys.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Inductance formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "psi / i", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "psi", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "L value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "inductance*0.95", "maxValue": "inductance*1.05", "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": "Reluctance", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The mathematical expression for the solenoid reluctance is $S =$[[0]].</p>\n<p>The value of $S$ is&nbsp;[[1]]&nbsp;H$^{-1}$.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Reluctance formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "N^2/L", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "l", "value": ""}, {"name": "n", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "S value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "reluctance*0.95", "maxValue": "reluctance*1.05", "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": "Stored energy", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The mathematical expression for the&nbsp;energy stored by the solenoid&nbsp;is $U =$[[0]].</p>\n<p>The value of $U$ is&nbsp;[[1]]&nbsp;Joules.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Energy formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "1/2 L i^2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "l", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "Energy value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "energy*0.95", "maxValue": "energy*1.05", "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": "Current for saturated 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 ferrite core saturates at a flux density of {Bsat} T.</p>\n<p>Determine the mathematical expression for the current that would produce this $B$-field: $i_{\\rm sat} =$[[0]].</p>\n<p>The value of $i_{\\rm sat}$ is&nbsp;[[1]]&nbsp;Amps.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Current formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "B 2 pi R /( mu_0 mu_r N)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "b", "value": ""}, {"name": "mu_0", "value": ""}, {"name": "mu_r", "value": ""}, {"name": "n", "value": ""}, {"name": "r", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "Current value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "isat*0.95", "maxValue": "isat*1.05", "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": "1_n_2", "useCustomName": true, "customName": "Post saturation inductance", "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 current is increased above the value that produces the saturated $B$-field, what is the impact upon the inductance?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "3", "showCellAnswerState": true, "choices": ["It continues to increase.", "It saturates (it remains constant)", "It starts to decrease."], "matrix": [0, 0, "1"], "distractors": ["No - the $\\Psi$ is a maximum and the inductance is inversely proportional to $i$.", "No - the $\\Psi$ is a maximum and the inductance is inversely proportional to $i$.", "Yes, because $\\Psi$ is a maximum and the inductance is inversely proportional to $i$."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Simple toriodal solenoid formulae and values", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}], "tags": [], "metadata": {"description": "Computation of quantities in a sequence of linked equations.", "licence": "All rights reserved"}, "statement": "<p>A torus made of a material with a relative permeability of {mur} has a wire wound around it {turns} times. The torus has circular cross section of area {areacm}&nbsp;cm$^2$ and the ring has an overall radius of {radius}&nbsp;cm. This solenoid is then connected to a power supply, and a current of {current}&nbsp;Amps is passed through the wire.</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 question is an example of a series of linked quantities.&nbsp;</p>\n<p style=\"text-align: center;\">${\\rm MMF}= N i=${mmf} Amps</p>\n<p style=\"text-align: center;\">$|H|=\\displaystyle{{\\rm MMF}\\over {\\rm path~length}}=\\displaystyle{Ni\\over2\\pi R}=${Hfield} A/m</p>\n<p style=\"text-align: center;\">$|B|=\\mu_0\\mu_r|H|=\\mu|H|=${Bfield} T</p>\n<p style=\"text-align: center;\">$\\phi=B A=${phi} Wb</p>\n<p style=\"text-align: center;\">$\\Psi = N \\phi=${Psi} Wb</p>\n<p style=\"text-align: center;\">$L = \\displaystyle{\\Psi\\over i}=${inductance} Henrys</p>\n<p style=\"text-align: center;\">$\\text{Stored energy}={1\\over2}Li^2=${energy1} Joules</p>\n<p style=\"text-align: left;\">In the redesign questions, it's simplest to write out the full equation dependence of the quantity being sought upon the variable being changed.</p>\n<p style=\"text-align: left;\">For the energy dependence upon the number of turns, we can write</p>\n<p style=\"text-align: left;\">$\\displaystyle \\text{Stored energy}={1\\over2}Li^2={1\\over 2}{\\Psi\\over i}i^2={1\\over 2}{N\\phi}i={1\\over 2}NBAi={1\\over 2}N\\mu HAi={1\\over 2}N\\mu {Ni\\over 2\\pi R}Ai={\\mu Ai^2 \\over 4\\pi R}N^2$</p>\n<p style=\"text-align: left;\">Thus, the energy stored is proportional to the number of turns squared, so, say, to increase the stored energy by a factor of 4 one would need to double the number of turns.&nbsp; This may not be feasible as there may be space constraints, and an increased number of turns will increase the electrical resistance of the coil.</p>", "rulesets": {}, "variables": {"pathlength": {"name": "pathlength", "group": "Ungrouped variables", "definition": "2*pi*rring", "description": "<p>Magnetic path length, m.</p>", "templateType": "anything"}, "energy2": {"name": "energy2", "group": "Ungrouped variables", "definition": "siground(energy1*4,2)", "description": "<p>Scaled up energy target, Joules.</p>", "templateType": "anything"}, "current": {"name": "current", "group": "Ungrouped variables", "definition": "random(0.1..1#0.1)", "description": "<p>Current through the core, Amps.</p>", "templateType": "anything"}, "newturns": {"name": "newturns", "group": "Ungrouped variables", "definition": "precround(sqrt(2*pathlength*energy2/(current^2*mu0*mur*area)),0)", "description": "<p>Number of turns required to yield higher energy.</p>", "templateType": "anything"}, "newmur": {"name": "newmur", "group": "Ungrouped variables", "definition": "newperm/mu0", "description": "<p>Revised relative permeability required for higher energy storage.</p>", "templateType": "anything"}, "radius": {"name": "radius", "group": "Ungrouped variables", "definition": "rring*100", "description": "<p>Radius of ring in cm.</p>", "templateType": "anything"}, "energy1": {"name": "energy1", "group": "Ungrouped variables", "definition": "siground(0.5*inductance*current^2,4)", "description": "<p>Stored energy under initial condtions, Joules.</p>", "templateType": "anything"}, "newperm": {"name": "newperm", "group": "Ungrouped variables", "definition": "siground((2*pathlength*energy2/(turns^2*current^2*area)),4)", "description": "<p>Revised permeability for higher energy storage, H/m.</p>", "templateType": "anything"}, "areacm": {"name": "areacm", "group": "Ungrouped variables", "definition": "siground(area*10^4,4)", "description": "<p>Cross sectional areas in cm^2.</p>", "templateType": "anything"}, "hfield": {"name": "hfield", "group": "Ungrouped variables", "definition": "mmf/pathlength", "description": "<p>Magnetising field strength in A/m.</p>", "templateType": "anything"}, "psi": {"name": "psi", "group": "Ungrouped variables", "definition": "phi*turns", "description": "<p>Flux linkage, Wb.</p>", "templateType": "anything"}, "turns": {"name": "turns", "group": "Ungrouped variables", "definition": "random(1000..2000)", "description": "<p>No. of turns of wire wrapped around the core.</p>", "templateType": "anything"}, "inductance": {"name": "inductance", "group": "Ungrouped variables", "definition": "psi/current", "description": "<p>Inductance of coil, Henrys.</p>", "templateType": "anything"}, "mmf": {"name": "mmf", "group": "Ungrouped variables", "definition": "turns current", "description": "<p>Magnetomotive force in Amps.</p>", "templateType": "anything"}, "area": {"name": "area", "group": "Ungrouped variables", "definition": "pi rcore^2", "description": "<p>cross-sectional area of core in m^2.</p>", "templateType": "anything"}, "bfield": {"name": "bfield", "group": "Ungrouped variables", "definition": "hfield*mur*mu0", "description": "<p>Magnetic flux density in Telsa.</p>", "templateType": "anything"}, "mu0": {"name": "mu0", "group": "Ungrouped variables", "definition": "4*pi*10^-7", "description": "<p>Permeability of free space in H/m</p>", "templateType": "anything"}, "phi": {"name": "phi", "group": "Ungrouped variables", "definition": "bfield*area", "description": "<p>Magnetic flux passing through the core, Wb.</p>", "templateType": "anything"}, "newcurrent": {"name": "newcurrent", "group": "Ungrouped variables", "definition": "siground(sqrt(2*pathlength*energy2/(turns^2*mu0*mur*area)),4)", "description": "<p>Revised current required to increase stored energy, Amps.</p>", "templateType": "anything"}, "rring": {"name": "rring", "group": "Ungrouped variables", "definition": "rcore+random(0.5..1.5)*0.01", "description": "<p>Radius of torus in m.</p>", "templateType": "anything"}, "rcore": {"name": "rcore", "group": "Ungrouped variables", "definition": "random(0.5..1.5#0.1)*0.01", "description": "<p>radius of core in m.</p>", "templateType": "anything"}, "mur": {"name": "mur", "group": "Ungrouped variables", "definition": "random(90..150#5)", "description": "<p>Relative permeability of core.</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["area", "areacm", "bfield", "current", "energy1", "energy2", "hfield", "inductance", "mmf", "mu0", "mur", "newcurrent", "newturns", "pathlength", "phi", "psi", "radius", "rcore", "rring", "turns", "newperm", "newmur"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Magnetomotive force", "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 magnetomotive force (MMF).</p>\n<p style=\"text-align: center;\">MMF$=$&nbsp;[[0]] Amps</p>\n<p style=\"text-align: center;\"></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "mmf", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "mmf*0.995", "maxValue": "mmf*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": "Magnetising field strength", "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 magnetising field strength.</p>\n<p style=\"text-align: center;\">$|\\vec{H}|=$&nbsp;[[0]] Amps/m</p>\n<p style=\"text-align: center;\"></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "H", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "hfield*0.995", "maxValue": "hfield*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": "Magnetic flux density", "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 magnetic flux density.</p>\n<p style=\"text-align: center;\">$|\\vec{B}|=$&nbsp;[[0]]&nbsp;Tesla</p>\n<p style=\"text-align: center;\"></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "B", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "bfield*0.995", "maxValue": "bfield*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": "Magnetic flux in the core", "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 magnetic flux in the core.</p>\n<p style=\"text-align: center;\">$\\phi=$&nbsp;[[0]]&nbsp;Wb</p>\n<p style=\"text-align: center;\"></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "phi", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "phi*0.995", "maxValue": "phi*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": "Flux linking the coil", "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 magnetic flux linking the coil (the flux linkage).</p>\n<p style=\"text-align: center;\">$\\Psi=$&nbsp;[[0]]&nbsp;Wb</p>\n<p style=\"text-align: center;\"></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "phi", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "psi*0.995", "maxValue": "psi*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": "Inductance", "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&nbsp;coil inductance.</p>\n<p style=\"text-align: center;\">$L=$&nbsp;[[0]]&nbsp;Henrys</p>\n<p style=\"text-align: center;\"></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "L", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "inductance*0.995", "maxValue": "inductance*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": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The solenoid as stated above stores {energy1}&nbsp;Joules of energy.&nbsp; However, for the application that the designer has in mind it needs to store at least {energy2}&nbsp;Joules.&nbsp; The plan is to change one part of the solenoid design.</p>"}, {"type": "gapfill", "useCustomName": true, "customName": "Redesign option 1", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If in order to increase the energy storage the designer will increase the number of turns, how many will be needed?</p>\n<p style=\"text-align: center;\">[[0]] turns</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Turns", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "newturns*0.995", "maxValue": "newturns*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": "Redesign option 2", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Alternatively, if in order to increase the energy storage the designer will increase the current, what value of current will be required?</p>\n<p style=\"text-align: center;\">[[0]]&nbsp;Amps</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Current", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "newcurrent*0.995", "maxValue": "newcurrent*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": "Redesign option 3", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finally, if in order to increase the energy storage the designer will swap the torus for a material with a different permeability, what value&nbsp;is required?</p>\n<p style=\"text-align: center;\">$\\mu=$ [[0]] H/m</p>\n<p style=\"text-align: center;\">$\\mu_r=$&nbsp;[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Permeability", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "newperm*0.995", "maxValue": "newperm*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"}, {"type": "numberentry", "useCustomName": true, "customName": "Relative permeability", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "newmur*0.995", "maxValue": "newmur*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", "type": "question"}, {"name": "Solenoid - reversed order question", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}], "tags": ["field", "flux", "mag", "mid1819", "solenoid"], "metadata": {"description": "Combine familiar questions in a slightly unfamiliar order.", "licence": "All rights reserved"}, "statement": "<p>A toroidal solenoid is constructed using an iron core, {turns}&nbsp;turns of wire carrying a current of {current}&nbsp;A. The torus has a circular cross-section of area {areacm}&nbsp;cm<sup>2</sup>, and diameter of {diametercm}&nbsp;cm.</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 equations linking the properties of a solenoid inductor should be familiar.&nbsp; This question starts in the familiar way,</p>\n<p>$\\displaystyle {\\rm MMF}=Ni$</p>\n<p style=\"text-align: center;\">$\\displaystyle |\\vec{H}|= {\\rm MMF\\over path~length}={Ni\\over \\pi d}$,</p>\n<p>where $d$ is the diameter of the ring.&nbsp;However, then the pathway differs in that we are provided with $\\phi$, and asked to calculate $B$ and $\\mu_r$.&nbsp; This requires some alegbra</p>\n<p style=\"text-align: center;\">$\\displaystyle \\phi =|\\vec{B}| A \\Rightarrow|\\vec{B}| = {\\phi\\over A}$</p>\n<p>and</p>\n<p style=\"text-align: center;\">$\\displaystyle&nbsp;|\\vec{B}|= \\mu&nbsp;|\\vec{H}|&nbsp;= \\mu_0\\mu_r |\\vec{H}| \\Rightarrow \\mu_r = {|\\vec{B}|\\over&nbsp;\\mu_0|\\vec{H}| }$.</p>", "rulesets": {}, "variables": {"mmf": {"name": "mmf", "group": "Ungrouped variables", "definition": "turns current", "description": "<p>Magnetomotive force, A</p>", "templateType": "anything"}, "bfield": {"name": "bfield", "group": "Ungrouped variables", "definition": "flux/area", "description": "<p>Magnetic flux density, T.</p>", "templateType": "anything"}, "hfield": {"name": "hfield", "group": "Ungrouped variables", "definition": "mmf/(pi diameter)", "description": "<p>Magnetising field strength, A/m.</p>", "templateType": "anything"}, "current": {"name": "current", "group": "Ungrouped variables", "definition": "random(0.5..1.0#0.05)", "description": "<p>Current throught the solenoid, A.</p>", "templateType": "anything"}, "diameter": {"name": "diameter", "group": "Ungrouped variables", "definition": "diametercm/100", "description": "<p>Diameter of the ring in m.</p>", "templateType": "anything"}, "areacm": {"name": "areacm", "group": "Ungrouped variables", "definition": "random(0.7..1.3#0.1)", "description": "<p>Cross-sectional area of core, cm^2.</p>", "templateType": "anything"}, "area": {"name": "area", "group": "Ungrouped variables", "definition": "areacm/10000", "description": "<p>Cross-sectional area of core, m^2.</p>", "templateType": "anything"}, "turns": {"name": "turns", "group": "Ungrouped variables", "definition": "random(60..90)*10", "description": "<p>Number of turns.</p>", "templateType": "anything"}, "flux": {"name": "flux", "group": "Ungrouped variables", "definition": "fluxu*10^-6", "description": "<p>Flux through core in Wb.</p>", "templateType": "anything"}, "fluxu": {"name": "fluxu", "group": "Ungrouped variables", "definition": "random(5..15)", "description": "<p>Flux through core in micro-Wb.</p>", "templateType": "anything"}, "mu0": {"name": "mu0", "group": "Ungrouped variables", "definition": "4 pi *10^-7", "description": "<p>Permeability of free space, H/m.</p>", "templateType": "anything"}, "diametercm": {"name": "diametercm", "group": "Ungrouped variables", "definition": "random(7..12)", "description": "<p>Diameter of the ring in cm.</p>", "templateType": "anything"}, "mur": {"name": "mur", "group": "Ungrouped variables", "definition": "bfield/hfield /mu0", "description": "<p>Relative permeability of the core.</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["area", "areacm", "bfield", "current", "diameter", "diametercm", "flux", "fluxu", "hfield", "mmf", "mu0", "mur", "turns"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "MMF", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate the magnetomotive force generate by the current in the coil.</p>\n<p style=\"text-align: center;\">MMF= [[0]] A</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "mmf", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "mmf*0.995", "maxValue": "mmf*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": "H-field", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate the magnetising field strength in the core.</p>\n<p style=\"text-align: center;\">$|\\vec{H}|=$[[0]] A/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "hfield", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [{"variable": "mmf", "part": "p0g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "hfield*0.995", "maxValue": "hfield*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": "B-field", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>If the flux passing through the core is {fluxu}$\\mu$Wb, calculate the magnetic flux density in the core.</p>\n<p style=\"text-align: center;\">$|\\vec{B}|=$[[0]]&nbsp;T</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "bfield", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "bfield*0.995", "maxValue": "bfield*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": "Relative permeability", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Hence, calculate the relative permeability of the core.</p>\n<p style=\"text-align: center;\">$\\mu_r=$[[0]]&nbsp;</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "mur", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [{"variable": "bfield", "part": "p2g0", "must_go_first": false}, {"variable": "hfield", "part": "p1g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "mur*0.995", "maxValue": "mur*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, 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