// Numbas version: finer_feedback_settings
{"name": "Solenoid - reversed order question", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Solenoid - reversed order question", "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": {}, "extensions": [], "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, "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": "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/"}]}