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{"name": "Basics of a magnetic field from a current in a wire.", "extensions": [], "custom_part_types": [], "resources": [["question-resources/current_clock.png", "/srv/numbas/media/question-resources/current_clock.png"], ["question-resources/current_anti.png", "/srv/numbas/media/question-resources/current_anti.png"], ["question-resources/current_mixed.png", "/srv/numbas/media/question-resources/current_mixed.png"], ["question-resources/current_angled_anti.png", "/srv/numbas/media/question-resources/current_angled_anti.png"], ["question-resources/current_angled_clock.png", "/srv/numbas/media/question-resources/current_angled_clock.png"], ["question-resources/current_no_direction.png", "/srv/numbas/media/question-resources/current_no_direction.png"], ["question-resources/current_spiral.png", "/srv/numbas/media/question-resources/current_spiral.png"], ["question-resources/wireandelectron.png", "/srv/numbas/media/question-resources/wireandelectron.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Basics of a magnetic field from a current in a wire.", "tags": [], "metadata": {"description": "Some equations, some vectors and some calculations.", "licence": "All rights reserved"}, "statement": "<p>This question relates to the magnetic fields generated by a current in a long, straight 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>The field from a long straight wire is given by the formula</p>\n<p style=\"text-align: center;\">$\\displaystyle \\left|\\vec{B}\\right|= {\\mu j\\over 2\\pi r}$,</p>\n<p>and it circulates according to the right-hand screw rule.&nbsp; Therefore the flux deminishes in magnitude as $1/r$ and circulates clock-wise as seen along the line of the wire looking in the direction of the current.</p>\n<p>The magnetising field strength is related to the magnetic flux density by</p>\n<p>$\\displaystyle \\vec{B}=\\mu\\vec{H}=\\mu_r\\mu_0\\vec{H}$</p>\n<p>so in the air (which essentially is the same as vacuum so far as magnetic fields are concerned),&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle \\left|\\vec{H}\\right|={j\\over 2\\pi r}$ and&nbsp;$\\displaystyle \\left|\\vec{B}\\right|={\\mu_0 j\\over 2\\pi r}$</p>\n<p>where $\\mu_0=4\\pi\\times10^{-7}$&nbsp;T.m/A.</p>\n<p>When there is a permeable piece of iron placed so that the point of interest is no longer in air, we have to take the new relative permeability into account.&nbsp; This changes only the magnetic flux density - it has no impact upon the magnetising field strength.</p>\n<p></p>", "rulesets": {}, "extensions": [], "variables": {"bfield": {"name": "bfield", "group": "Ungrouped variables", "definition": "mu0*current/(2 pi distance)", "description": "<p>Flux density at the electron, T.</p>", "templateType": "anything"}, "current": {"name": "current", "group": "Ungrouped variables", "definition": "random(0..1#0.1)+1", "description": "<p>Current in the wire, Amps.</p>", "templateType": "anything"}, "distancemm": {"name": "distancemm", "group": "Ungrouped variables", "definition": "random(0..1#0.1)+1", "description": "<p>Distance of the moving electron from the wire, mm</p>", "templateType": "anything"}, "distance": {"name": "distance", "group": "Ungrouped variables", "definition": "distancemm/1000", "description": "<p>Distance of the moving electron from the wire, m</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"}, "hfield": {"name": "hfield", "group": "Ungrouped variables", "definition": "current/2/pi/distance", "description": "", "templateType": "anything"}, "mur": {"name": "mur", "group": "Ungrouped variables", "definition": "random(50..200#0.1)", "description": "<p>Relative permeability of iron close to the wire.</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["bfield", "current", "distance", "distancemm", "mu0", "hfield", "mur"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": true, "customName": "Schematic", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of the following is an illustrations of the magnetic flux from the wire? The current is {current}&nbsp;A into the page.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "6", "showCellAnswerState": true, "choices": ["<img src=\"resources/question-resources/current_spiral.png\"/>", "<img src=\"resources/question-resources/current_no_direction.png\"/>", "<img src=\"resources/question-resources/current_angled_clock.png\"/>", "<img src=\"resources/question-resources/current_angled_anti.png\"/>", "<img src=\"resources/question-resources/current_anti.png\"/>", "<img src=\"resources/question-resources/current_clock.png\"/>"], "matrix": [0, 0, 0, 0, "0", "1"], "distractors": ["Although charged particles may have a helical path in a field, the field itself is not spiral.", "There are no directions indicated here - it cannot be correct.", "No - the wire has cylindrical symmetry, therefore so must the the field.", "No - the wire has cylindrical symmetry, therefore so must the the field.", "No - this direction of the field follows the right-hand screw rule for the current out of the page.", "Yes - this follows the right-hand screw rule for the current into the page."]}, {"type": "gapfill", "useCustomName": true, "customName": "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>Complete&nbsp;the equation for the flux density a distance $r$ from the wire.&nbsp; You may use the symbol $\\mu$ (mu) for permeability, $\\epsilon$ (epsilon) for the permittivity, $A$ for the cross-sectional area of the wire and use $j$ for current.</p>\n<p style=\"text-align: center;\">$|\\vec{B}|=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "B formula", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "mu j /(2 pi r)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "j", "value": ""}, {"name": "mu", "value": ""}, {"name": "r", "value": ""}]}], "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>What is the magnitude of the magnetizing field strength a distance {distancemm}&nbsp;mm from a long straight wire carrying a constant current of {current}&nbsp;amps.</p>\n<p style=\"text-align: center;\">$|H|=$[[0]]&nbsp;A/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Hfield", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "hfield*0.99", "maxValue": "hfield*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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>What is the corresponding magnetic flux density at the same point in space?</p>\n<p style=\"text-align: center;\">$|B|=$[[0]]&nbsp;T</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Bfield", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "bfield*0.99", "maxValue": "bfield*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Iron", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A piece of iron is placed so that the point at which you have evaluated the magnitudes of the magnetic fields lies within it.&nbsp; If the relative magnetic permeability of the iron is {mur}, determine revised values for the fields:</p>\n<p style=\"text-align: center;\">$|H|=$[[0]]&nbsp;A/m</p>\n<p style=\"text-align: center;\">$|B|=$[[1]]&nbsp;T</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "New H", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "hfield*0.99", "maxValue": "hfield*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "New B", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "bfield*mur*0.99", "maxValue": "bfield*mur*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}]}