// Numbas version: finer_feedback_settings {"name": "Ejercicio interactivo FIS2227 Semana 1", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "FIS2227_S1_Numbas", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "An\u00e1lisis cualitativo de la fuerza el\u00e9ctrica FIS2227", "extensions": [], "custom_part_types": [], "resources": [["question-resources/CoulombForce1.png.png", "/srv/numbas/media/question-resources/CoulombForce1.png.png"], ["question-resources/CoulombForce2.png.png", "/srv/numbas/media/question-resources/CoulombForce2.png.png"], ["question-resources/CoulombForce3.png.png", "/srv/numbas/media/question-resources/CoulombForce3.png.png"], ["question-resources/CoulombForce4.png.png", "/srv/numbas/media/question-resources/CoulombForce4.png.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}], "tags": ["coulomb", "elec", "field", "force", "mid1718"], "metadata": {"description": "

Conceptos y cálculo en el contexto de la fuerza eléctrica y campo eléctrico. Incluyendo magnitudes de los vectores y sus unidades

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Esta pregunta se enfoca en la comprensión de los nombres y unidades de aquellos símbolos relevantes en el contexto de la fuerza eléctrica, la habilidad para realizar cálculos de cantidades fisicas de la electrostática y evaluar las direcciones de las fuerzas involucradas. Todo esto con el bojetivo de reforzar el contenido necesario para el buen desempeño en el uso de las simulaciones correspondientes a la semana 1.

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Cuando proporcione respuestas numéricas, puede expresarlas usando notación científica. Exprese los valores con cuatro cifras significativas y use los valores de las constantes físicas que se proporcionan en los PDF y videos del curso de Laboratorio y el teórico.

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The Coulomb field is for a point charge (the equation does not generally apply to all charge arrangements):

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
SymbolDescriptionUnits
$E$Electric field strengthV/m (or N/C)
$q$Point chargeC
$\\varepsilon_0$Permittivity of free spaceF/m
$\\varepsilon_r$Relative permittivity of medium betweem the point charge and where the field is being establishednone
$r$Distance from the point charge - it's definitely not a radius!m
$\\hat{r}$This is the unit radial vector.  It is not a displacement (which would have units of m).none
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In the calculation of the magnitude of the electric field strength, care has to be taken to correctly account for units.

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From the electric field, a force can be obtained using $F=qE$.  For this problem the field has already been obtained, and all that's required is to multiply this by the magnitude of the second point charge.

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Since the charges are opposite in sign, they attract.

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Second point charge in C.

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Point charge in C.

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Electric field at the distant point in N/C.

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Charge on the second point charge in muC.

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Radial distance from the point charge, mm.

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Radial distance from the point charge, m.

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Magnitude of force on second point charge, N.

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Permittivity of free space, F/m.

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Point charge in micro-C.

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Como ya sabemos, la Ley de Coulomb puede ser expresada de la siguente manera. Se recomienda revisar los videos de las clases 1 y 2 de la semana 1 y sus respectivos PDF.

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$\\displaystyle \\vec{E}= {q\\over 4 \\pi \\varepsilon_0 \\varepsilon_r r^2}\\hat{r}$.

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$\\vec{E}$ es [[0]] con unidad de [[1]]

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$q$ es [[2]] con unidad de [[3]]

\n

$\\varepsilon_0$ es [[4]] con unidad de [[5]]

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$\\varepsilon_r$ es [[6]] con unidad de [[7]]

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$r$ es [[8]] con unidad de [[9]]

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$\\hat{r}$ es [[10]] con unidad de [[11]]

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Calcule la magnitud del campo eléctrico a {rmm} mm de distancia de una carga puntual de {q1mu} μC en el vacío. Ingrese el valor numérico completo.

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$|\\vec{E}|=$ [[0]] [[1]]

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Cuál es la ecuación correcta para expresar la fuerza eléctrica que una segunda carga, $q_2$ experimentaría si es situada en un campo eléctrico $E_1$, producido por la carga puntual del inciso anterior?

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$F=$[[0]]

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Ingrese sub índice b de una símbolo A como A_b.

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Calcule la magnitud de una fuerza que experimentaría una carga puntual de {q2mu} μC situada a {rmm} mm de distancia de otra carga puntual {q1mu} μC en el vacío.

\n

$|\\vec{F}|=$ [[0]] [[1]]

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Calculo simple de una fuerza de Coulomb entre dos cargas puntuales, enfocado en la importancia de las unidades de medida y la inclusión de las constantes correctas.

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Esta pregunta se enfoca en el análisis de la Ley de Coulomb para la descripción cuantitativa de la Fuerza eléctrica entre, para este caso, dos cargas puntuales estacionarias.
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Cuando proporcione respuestas numéricas, puede expresarlas usando notación científica. Exprese los valores con cuatro cifras significativas y use los valores de las constantes físicas que se proporcionan en los PDF y videos del curso de Laboratorio y el teórico. Consideraremos el valor de la permitividad relativa del aire como \"\\varepsilon=1.0005.
", "advice": "

Si obtuvo una respuesta incorrecta, recuerde tener presente lo siguiente:

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El campo eléctrico $E$ debido a una carga puntual es

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$\\displaystyle{q\\over 4 \\pi \\varepsilon_0 \\varepsilon_r r^2}$

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donde $r$ es la distancia radial con respecto a la carga fuente (la que produce el campo eléctrico, la otra se denomina carga de prueba). La fuerza experimentada en un campo eléctrico es en este contexto $\\vec{F}=q\\vec{E}$, por lo tanto, la fuerza ejercida sobre una carga $q_1$ debido al campo que produce la carga fuente $q_2$ (cualquiera puede ser considerada fuente o carga de prueba), tiene una magnitud de

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$\\displaystyle q_1 {q_2\\over 4 \\pi \\varepsilon_0 \\varepsilon_r r^2}$.

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Debido a que generalmente $\\varepsilon_r\\ge1$, cualquier material entre las dos cargas tiende a reducir la fuerza experimentada entre las cargas en relación a la misma situación pero en el vacío. Es importante notar que la pregunta se refiere al porcentaje en el cual la fuerza se ha reducido, no el porcentaje de la fuerza que se obtiene finalmente.

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La fuerza debida a la gravedad es $mg$ y se dirije hacia el centro de la Tierra, de este modo, uno puede calcular la fuerza debida a la presencia de un campo eléctrico y trabajar enfocandose en el valor de la masa cuando, al ser multiplicada por $g$, tiene la misma magnitud.

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Approximate value for the acceleration due to gravity on Earth's surface (m/s/s).

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Permitividad del espacio vacío en F/m.

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Mass that would balance the force between the charges on Earth (kg).

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Distance of the second point charge from the first in cm.

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Randomised relative permittivity of material substituting for air (no units)

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Magnitude of charge for which the electric field is originating in $\\mu$C, randomised in steps of 0.5$\\mu$C from 0.5 to 2.5$\\mu$C, but different from $q_1$.

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Relative permittivity of air (dimensionless quantity).

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Magnitude of charge for which the force is to be obtained in $\\mu$C, randomised in steps of 0.5$\\mu$C from 0.5 to 2.5.

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Coulomb force on one charge due to another, in N, is given by $q_1q_2/4\\pi\\varepsilon r^2$.

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Usando la Ley de Coulomb, calcule la fuerza ejercida sobre una carga puntual de {q1} $\\mu$C debida al el campo eléctrico creado por una carga eléctrica puntual de {q2} cuando la separación de ellas es de {r1} cm (de aire).

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$|\\vec{F}| =$ [[0]] Newtons. 

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¿Cuál es el porcentaje de reducción de la fuerza cuando el aire es reemplazado por un material cuya permitividad eléctrica relativa es $\\varepsilon_r =\\var{epsmat}$?  

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La fuerza experimenta una reducción de  [[0]] %

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Si en este caso particular la fuerza gravitacional en la superficie de la tierra (o en sus cercanías) se equilibra con la fuerza eléctrica en una carga puntual $\\var{q1}\\,\\mu\\text{C}$ debido a otra carga puntual $\\var{q2}\\,\\mu\\text{C}$ (la fuente) ¿cuál es su masa? considere que la aceleración gravitacionesl es {g} N/kg.

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La masa en equilibrio traslacional es [[0]] kg

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