// Numbas version: finer_feedback_settings
{"name": "Superposition of electric fields", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Picture_1.png", "/srv/numbas/media/question-resources/Picture_1.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Superposition of electric fields", "tags": ["coulomb", "elec", "field", "tut1", "vector", "Vector"], "metadata": {"description": "Evaluation of the vector superposition of fields arising from four point-charges.&nbsp; This is a problem of vector addition, vector magnitudes and scalar (dot) products with a bit of trigonometry thrown in for good measure.", "licence": "All rights reserved"}, "statement": "<p style=\"text-align: center;\"><img src=\"resources/question-resources/Picture_1.png\" width=\"400pt\"/></p>\n<p>A square of side length {sidecm} cm has charges of different magnitudes placed at its four corners. Clockwise from the top right as viewed from above these are $q_1$ to $q_4$, with values {q1}, {q2}, {q3} and {q4} nC. In this question, you are required to determine the total electric field, including both magnitude and direction, at the centre of the square due to this arrangement of point charges.</p>\n<p>This question is a relatively complicated example of application of the principle of superposition.</p>\n<p>You should use the values of the physical constants provided in the module notes, assume the medium is air, quote all answers to 4 significant figures and you may express values in scientific format.</p>", "advice": "<p style=\"text-align: center;\"><img src=\"resources/question-resources/Picture_1.png\" width=\"400pt\"/></p>\n<p>This is a problem of superposition of four different fields, which amounts to the sum of four vectors.&nbsp; Each field is an expression of Coulomb's Law, so that the pre-factor is</p>\n<p style=\"text-align: center;\">$\\displaystyle {q_i\\over 4\\pi\\varepsilon_0 r^2}$,</p>\n<p>where since the point of interest is the centre of the square, the distance $r$ is the same for each point-charge (in this case {side*100}/$\\sqrt{2}\\approx$ {siground(r*100,4)} cm). In each case the field points radially away from the point-charge so that for $q_1$ it is down and left in equal measures, for $q_2$ it is up and to the left, and so on.&nbsp; For negative charges the sign of $q$ can be thought of reversing the direction (fields converge on negative point charges).&nbsp; Take care in determining the direction and note that diagrams generally help!</p>\n<p>The value of $E$ can be readily obtained and the direction in each case given by</p>\n<p style=\"text-align: center;\">$\\displaystyle{1\\over\\sqrt{2}}\\left(\\pm \\hat{i} \\pm \\hat{j}\\right)$,&nbsp;</p>\n<p>with the combinations of $\\pm$ depending upon which charge we're considering and the $\\sqrt{2}$ factor coming from the fact that this is a unit vector.</p>\n<p style=\"text-align: left;\">Once each vector field has been obtained they can be summed by component (apply the principle of superposition) giving the total $E$-field at the centre of the square.</p>\n<p>Finally the angle with the line joining $q_2$ and $q_4$ can be obained by noting that the dot product of the total field with the direction of the displacement from $q_2$ to $q_4$ yields an angle:</p>\n<p style=\"text-align: center;\">$\\displaystyle{\\vec{E}.\\left(-\\frac{\\hat{i}}{\\sqrt{2}}+\\frac{\\hat{j}}{\\sqrt{2}}\\right)=\\left|\\vec{E}\\right|\\cos(\\theta)}$</p>\n<p style=\"text-align: left;\">so</p>\n<p style=\"text-align: center;\">$\\displaystyle{-E_x+E_y=\\sqrt{2}\\left|\\vec{E}\\right|\\cos(\\theta)\\Rightarrow \\theta=\\cos^{-1}\\left(\\frac{E_y-E_x}{\\sqrt{2}\\left|\\vec{E}\\right|}\\right)}$.</p>\n<p style=\"text-align: left;\">It then only remains to determine the value of theta that lies in the required angle range.</p>", "rulesets": {}, "extensions": [], "variables": {"Ey1": {"name": "Ey1", "group": "Ungrouped variables", "definition": "Ex1", "description": "<p>$y$-component of the E-field from q1(N/C).</p>", "templateType": "anything"}, "q3": {"name": "q3", "group": "Ungrouped variables", "definition": "random(1..10#1 except q1 except q2)*random(-1..1#2)", "description": "<p>Point charge in the bottom left corner, nC.</p>", "templateType": "anything"}, "epsair": {"name": "epsair", "group": "Ungrouped variables", "definition": "1.0005", "description": "<p>Relative permittivity of air.</p>", "templateType": "anything"}, "Emag": {"name": "Emag", "group": "Ungrouped variables", "definition": "sqrt(Extotal^2+Eytotal^2)", "description": "<p>Magnitude of the field at the centre.</p>", "templateType": "anything"}, "sidecm": {"name": "sidecm", "group": "Ungrouped variables", "definition": "random(5..15#1)", "description": "<p>Length of side of square in cm.</p>", "templateType": "anything"}, "Ex2": {"name": "Ex2", "group": "Ungrouped variables", "definition": "-({qq2}*{k}/{r}^2)/sqrt(2)", "description": "<p>$x$-component of the E-field from q2 (N/C).</p>", "templateType": "anything"}, "thetar": {"name": "thetar", "group": "Ungrouped variables", "definition": "arccos((-Extotal/sqrt(2)+Eytotal/sqrt(2))/Emag)", "description": "<p>Angle between the line between q2 and q4 and the E-field</p>", "templateType": "anything"}, "Ey4": {"name": "Ey4", "group": "Ungrouped variables", "definition": "-Ex4", "description": "<p>$y$-component of the E-field from q4 (N/C).</p>", "templateType": "anything"}, "Ey2": {"name": "Ey2", "group": "Ungrouped variables", "definition": "-Ex2", "description": "<p>$y$-component of the E-field due to q2 (N/C).</p>", "templateType": "anything"}, "Ex4": {"name": "Ex4", "group": "Ungrouped variables", "definition": "({qq4}*{k}/{r}^2)/sqrt(2)", "description": "<p>$x$-component of the E-field from q4 (N/C).</p>", "templateType": "anything"}, "Extotal": {"name": "Extotal", "group": "Ungrouped variables", "definition": "(Ex1+Ex2+Ex3+Ex4)", "description": "", "templateType": "anything"}, "q4": {"name": "q4", "group": "Ungrouped variables", "definition": "random(1..10#1 except q1 except q2 except q3)*random(-1..1#2)", "description": "<p>Point charge in the top left corner, nC.</p>", "templateType": "anything"}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "side/sqrt(2)", "description": "<p>Distance from the charges to the centre of the square in m.</p>", "templateType": "anything"}, "q2": {"name": "q2", "group": "Ungrouped variables", "definition": "random(1..10#1 except q1)*random(-1..1#2)", "description": "<p>Point charge in bottom right corner, nC.</p>", "templateType": "anything"}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "if(thetad>270,\n  360-thetad,\n  if(thetad>180,\n    thetad-180,\n    if(thetad>90,\n      180-thetad,\n      thetad)\n)\n)", "description": "", "templateType": "anything"}, "Ex1": {"name": "Ex1", "group": "Ungrouped variables", "definition": "-(qq1*k/r^2)/sqrt(2)", "description": "<p>$x$-component of the E-field from q1 (N/C).</p>", "templateType": "anything"}, "Eytotal": {"name": "Eytotal", "group": "Ungrouped variables", "definition": "Ey1+Ey2+Ey3+Ey4", "description": "", "templateType": "anything"}, "eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "8.854*10^-12", "description": "<p>Permittivity of free space in F/m to 4 significant figures.</p>", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "1/(4*pi*eps0*epsair)", "description": "<p>The constant, $1/4\\pi\\varepsilon$ in units of m/F.</p>", "templateType": "anything"}, "Ey3": {"name": "Ey3", "group": "Ungrouped variables", "definition": "Ex3", "description": "<p>$y$-component of the E-field from q3 (N/C).</p>", "templateType": "anything"}, "Ex3": {"name": "Ex3", "group": "Ungrouped variables", "definition": "({qq3}*{k}/{r}^2)/sqrt(2)", "description": "<p>$x$-component of the E-field from q3 (N/C).</p>", "templateType": "anything"}, "q1": {"name": "q1", "group": "Ungrouped variables", "definition": "random(1..10#1)*random(-1..1#2)", "description": "<p>Point charge in top right corner in nC.</p>", "templateType": "anything"}, "thetad": {"name": "thetad", "group": "Ungrouped variables", "definition": "thetar*180/pi", "description": "", "templateType": "anything"}, "rsq": {"name": "rsq", "group": "Ungrouped variables", "definition": "r*r", "description": "<p>r^2, cm</p>", "templateType": "anything"}, "side": {"name": "side", "group": "Ungrouped variables", "definition": "sidecm/100", "description": "<p>Side length in m.</p>", "templateType": "anything"}, "qq1": {"name": "qq1", "group": "Ungrouped variables", "definition": "q1*10^-9", "description": "<p>q1 in C</p>", "templateType": "anything"}, "qq2": {"name": "qq2", "group": "Ungrouped variables", "definition": "q2*10^-9", "description": "<p>q2 in C</p>", "templateType": "anything"}, "qq3": {"name": "qq3", "group": "Ungrouped variables", "definition": "q3*10^-9", "description": "<p>q3 in C</p>", "templateType": "anything"}, "qq4": {"name": "qq4", "group": "Ungrouped variables", "definition": "q4*10^-9", "description": "<p>q4 in C</p>", "templateType": "anything"}}, "variablesTest": {"condition": "theta>0", "maxRuns": 100}, "ungrouped_variables": ["Emag", "eps0", "epsair", "Ex1", "Ex2", "Ex3", "Ex4", "Extotal", "Ey1", "Ey2", "Ey3", "Ey4", "Eytotal", "k", "q1", "q2", "q3", "q4", "qq1", "qq2", "qq3", "qq4", "r", "rsq", "side", "sidecm", "theta", "thetad", "thetar"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Field due to first charge", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the electric field at the centre of the square due to $q_1$ ({q1}nC).</p>\n<p style=\"text-align: center;\">$E_x(q_1)=$[[0]]V/m</p>\n<p style=\"text-align: center;\">$E_y(q_1)=$[[1]]V/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Ex1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Ex1*0.995", "maxValue": "Ex1*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": "Ey1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Ey1*0.995", "maxValue": "Ey1*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": "Field due to second charge", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the electric field at the centre of the square due to $q_2$ ({q2}nC).</p>\n<p style=\"text-align: center;\">$E_x(q_2)=$[[0]]V/m</p>\n<p style=\"text-align: center;\">$E_y(q_2)=$[[1]]V/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Ex2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Ex2}*0.995", "maxValue": "{Ex2}*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": "Ey2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Ey2}*0.995", "maxValue": "{Ey2}*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": "Field due to third charge", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the electric field at the centre of the square due to $q_3$ ({q3}nC).</p>\n<p style=\"text-align: center;\">$E_x(q_3)=$[[0]]V/m</p>\n<p style=\"text-align: center;\">$E_y(q_3)=$[[1]]V/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Ex3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Ex3}*0.995", "maxValue": "{Ex3}*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": "Ey3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Ey3}*0.995", "maxValue": "{Ey3}*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": "Field due to fourth charge", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the electric field at the centre of the square due to $q_4$ ({q4}nC).</p>\n<p style=\"text-align: center;\">$E_x(q_4)=$[[0]]V/m</p>\n<p style=\"text-align: center;\">$E_y(q_4)=$[[1]]V/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Ex4", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Ex4}*0.995", "maxValue": "{Ex4}*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": "Ey4", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Ey4}*0.995", "maxValue": "{Ey4}*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": "Total field", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the total electric field at the centre of the square due to the all four charges.</p>\n<p style=\"text-align: center;\">$E_x=$[[0]]V/m</p>\n<p style=\"text-align: center;\">$E_y=$[[1]]V/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Extotal", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "({Ex1}+{Ex2}+{Ex3}+{Ex4})0.995", "maxValue": "({Ex1}+{Ex2}+{Ex3}+{Ex4})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": "Eytotal", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "(Ey1+Ey2+Ey3+Ey4)*0.995", "maxValue": "(Ey1+Ey2+Ey3+Ey4)*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": "Angle", "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 angle, $\\theta$, between the direction of the $E$-field and the line joining the charges $q_2$ ({q2}nC) and $q_4$ ({q4}nC)?&nbsp; Express your answer as an angle in degrees in the range $0^\\circ\\le\\theta\\le90^\\circ$.</p>\n<p style=\"text-align: center;\">$\\theta=$[[0]]$^\\circ$.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "theta", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "theta*0.995", "maxValue": "theta*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", "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/"}]}