// Numbas version: finer_feedback_settings
{"name": "Distribuci\u00f3n cont\u00ednua y Ley de Gauss", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Distribuci\u00f3n cont\u00ednua y Ley de Gauss", "tags": ["elec", "field", "flux", "Gauss", "gauss"], "metadata": {"description": "<p>Preguntas y actividades relativas a los principios de aplicaci&oacute;n de la Ley de Gauss a sistemas f&iacute;sicos simples.</p>", "licence": "None specified"}, "statement": "<p>La Ley de Gauss es una poderosa expresi&oacute;n general de la matem&aacute;tica y la f&iacute;sica, que relaciona la distribuci&oacute;n de cargas fuente con la intensidad del campo el&eacute;ctrico, $\\vec{E}$. La formulaci&oacute;n matem&aacute;tica de la Ley relaciona el flujo del campo el&eacute;ctrico a trav&eacute;s de una superficie cerrada, $\\phi_{\\rm electric}$ con la carga contenida dentro de esa superficie, $q$.</p>\n<p>Cuando ingrese respuestas num&eacute;ricas, puede expresarlas usando notaci&oacute;n cient&iacute;fica. Expresar valores con cuatro cifras significativas y usar los valores de las constantes f&iacute;sicas como se indica en las notas del curso en la semana 2.&nbsp;</p>", "advice": "<p>Esto es en parte un problema matem&aacute;tico y en parte f&iacute;sico, pero se centra en la formulaci&oacute;n de la Ley de Gauss como</p>\n<p style=\"text-align: center;\">$\\displaystyle \\phi_{\\rm electric}=\\oint_S \\vec{E}.d\\vec{A}={q\\over\\varepsilon}$,</p>\n<p>donde $\\phi_{\\rm electric}$ es el flujo de campo el&eacute;ctrico a trav&eacute;s de la superficie gaussiana cerrada (una superficie abstracta y no f&iacute;sica), $S$, $\\vec{E}$ es el campo el&eacute;ctrico a trav&eacute;s de $S$, $d\\vec{A}$ es un elemento del &aacute;rea superficial, $q$ es la carga total contenida dentro de $S$ y $\\varepsilon$ es la permitividad.</p>\n<p>Para abordar la parte num&eacute;rica de este &iacute;tem, simplemente notamos que la distribuci&oacute;n de la carga no es relevante (la ley de Gauss se aplica cualquiera que sea la distribuci&oacute;n de la carga dentro de la superficie cerrada) y entonces podemos usar</p>\n<p style=\"text-align: center;\">$\\displaystyle |\\phi_{\\rm electric}|=\\left|{q\\over\\varepsilon}\\right|=\\left|{e N_{\\rm electron}\\over\\varepsilon}\\right|$,</p>\n<p style=\"text-align: left;\">donde $e=1.6\\times10^{-19}$C es el valor de la carga el&eacute;ctrica fundamental.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"flux": {"name": "flux", "group": "Ungrouped variables", "definition": "nelec*qe/eps0", "description": "<p>flux in V.m</p>", "templateType": "anything", "can_override": false}, "chargee": {"name": "chargee", "group": "Ungrouped variables", "definition": "charge/qe", "description": "<p>Number of electrons within the Gaussian surface.</p>", "templateType": "anything", "can_override": false}, "eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "decimal(8.854*10^(-12))", "description": "<p>Permittivity of free space, F/m</p>", "templateType": "anything", "can_override": false}, "qe": {"name": "qe", "group": "Ungrouped variables", "definition": "decimal(1.6*10^-19)", "description": "<p>Charge on an electron, C.</p>", "templateType": "anything", "can_override": false}, "nelec": {"name": "nelec", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "<p>Number of electrons inside the Gaussian surface.</p>", "templateType": "anything", "can_override": false}, "charge": {"name": "charge", "group": "Ungrouped variables", "definition": "flux * eps0", "description": "<p>Charge contained within the Gaussian surface in C.</p>", "templateType": "anything", "can_override": false}, "fluxnm": {"name": "fluxnm", "group": "Ungrouped variables", "definition": "siground(flux*10^9,4)", "description": "<p>Flux through Gaussian surface in V.nm</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["charge", "chargee", "eps0", "flux", "fluxnm", "qe", "nelec"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Flujo a trav\u00e9s de una superficie", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>El flujo a trav&eacute;s de la superficie expresado como una integral en t&eacute;rminos de la intensidad del campo el&eacute;ctrico $\\vec{E}$ y los elementos de la superficie, $d\\vec{A}$ es un integral sobre la superficie cerrada, $S$, expresada como</p>\n<p style=\"text-align: center;\">$\\displaystyle \\phi=\\oint_S$[[0]]</p>\n<p style=\"text-align: left;\">Su respuesta debe ingresarse usando \"dot(a,b)'' si usted piensa que el producto escalar entre estas cantidades es la opci&oacute;n correcta y \"X(a,b)\" si usted piensa que el producto vectorial o producto cruz es la opci&oacute;n correcta. Aqu&iacute;, a y b son los s&iacute;mbolos de los vectores.</p>\n<p style=\"text-align: left;\">Importante: $\\vec{E}$ (debe ser ingresado como <strong>campoE</strong>) y $d\\vec{A}$ (debe se ringreesado como <strong>dA</strong>)</p>\n<p style=\"text-align: left;\">La idea de este &iacute;tem es, al usar los motores de simulaci&oacute;n del curso, usted pueda comprender qu&eacute; es lo que se est&aacute; evaluando realmente con esta ley f&iacute;sica.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Flujo de campo a trav\u00e9s de una superficie", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "dot(campoE,dA)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "campoe", "value": ""}, {"name": "da", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "T\u00e9rmino correspondiente a la carga fuente", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>El flujo a trav&eacute;s de la superficie es igual a una cantidad que depende de la carga contenida dentro de la superficie, $q$, y la permitividad del espacio que contiene la carga, $\\varepsilon$ (epsilon). esta cantidad es</p>\n<p style=\"text-align: center;\">[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Termino de carga", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "q/epsilon", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "epsilon", "value": ""}, {"name": "q", "value": ""}]}], "sortAnswers": false}, {"type": "m_n_2", "useCustomName": true, "customName": "Elecci\u00f3n de la superficie Gaussiana", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Al seleccionar una superficie gaussiana, se pueden tener en cuenta varios factores. Indique al menos 1 condici&oacute;n t&iacute;pica. Tenga en cuenta que se descuentan puntos (-1) por respuestas incorrectas.</p>", "minMarks": "-100", "maxMarks": "2", "shuffleChoices": true, "displayType": "checkbox", "displayColumns": "2", "minAnswers": "1", "maxAnswers": 0, "warningType": "prevent", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["La simetr&iacute;a del sistema.", "Debe considerarse el volumen encerrado por la superficie Gaussiana tan grande como sea posible.", "Debe considerarse el volumen encerrado por la superficie Gaussiana tan peque&ntilde;o como sea posible.", "La superficie debe ser una esfera.", "Debe tener supercicies planas (como el caso de un cubo)", "Contribuye a que el flujo pase a trav&eacute;s de la superficie paralelo al vector normal de la superficie.", "Siempre existe una elecci&oacute;n correcta para la superficie Gaussiana a usar. Solo debemos trabajar en pensar cu&aacute;l es esta."], "matrix": ["1", "-1", 0, "-1", "-1", "1", "-1"], "distractors": ["\u00a1Necesitamos hacer la integral integrable!", "El volumen es usualmente irrelevante.", "El volumen es usualmente irrelevante.", "Solo se aplica a la soluci\u00f3n anal\u00edtica para un arreglo de carga puntual o esf\u00e9rica.", "Generalmente no.", "Esto es generalmente \u00fatil ya que hace que la integraci\u00f3n sea sencilla.", "La formulaci\u00f3n de la Ley de Gauss es general y no es exclusiva de una superficie espec\u00edfica: solo buscamos algo para lo que podamos hacer los c\u00e1lculos..."]}, {"type": "gapfill", "useCustomName": true, "customName": "La carga el\u00e9ctrica fuente", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Si se tiene que el campo el&eacute;ctrico de una distribuci&oacute;n de carga da lugar a un flujo el&eacute;ctrico a trav&eacute;s de una superficie gaussiana de {fluxnm} volts-nan&oacute;metros. Entonces, si la carga est&aacute; en el vac&iacute;o, &iquest;cu&aacute;l es la cantidad total de carga dentro de la superficie gaussiana?</p>\n<p style=\"text-align: center;\">$|Q|=$&nbsp;[[0]] Coulombs</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Charge", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "charge*0.995", "maxValue": "charge*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": "N\u00famero de electrones", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Si la carga de la pregunta anterior se debe a un conjunto de electrones, &iquest;cu&aacute;ntos hay dentro de la superficie gaussiana?</p>\n<p style=\"text-align: center;\">$n_{\\rm electrones}=$ [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "N", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "nelec", "maxValue": "nelec", "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/"}, {"name": "Marcelo Calder\u00f3n", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/17160/"}]}]}], "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}, {"name": "Marcelo Calder\u00f3n", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/17160/"}]}