// Numbas version: exam_results_page_options
{"name": "Simple toriodal solenoid formulae and values", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Simple toriodal solenoid formulae and values", "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": {}, "extensions": [], "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": 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