Name: charge conservation and current flow
Uploaded: 2023-09-18T17:11:18.000Z
Duration: 1 min 20 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

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Motion and Stability- Forces and Interactions

PS.PSc.6.3

Continuity Equation

La densidad de corriente es la cantidad total de corriente que fluye por unidad de área de sección transversal. Por lo tanto, la corriente total que pasa a través de un área de sección transversal se puede expresar como la integral de superficie de la densidad de corriente.
Ahora, la conservación de la carga requiere que la corriente total que fluye de un volumen dado sea igual a la tasa de disminución de la carga dentro de ese volumen.
Expresando la carga total en términos de la densidad de carga volumétrica, la ecuación se modifica. Dado que la densidad de carga es una función espacial, usando la regla de Leibniz, su derivada temporal se puede mover dentro de la integral.
Aplicando el teorema de divergencia al lado izquierdo de la ecuación, se convierte la integral de superficie cerrada en una integral de volumen. Esta relación es válida para cualquier volumen; Como resultado, los integrandos son iguales.
La divergencia de la densidad de corriente es igual a la tasa negativa de cambio de la densidad de carga volumétrica. Este enunciado matemático de la conservación de la carga local se denomina ecuación de continuidad.
Para corrientes constantes, la densidad de carga es invariable con el tiempo. Entonces, la divergencia de la densidad de corriente es cero.

<ol>
	<li>Griffiths, David J., Introducción a la electrodinámica, CA: Pearson. pp. 222</li>
	<li>Ida, Nathan, Ingeniería Electromagnética, 3ª Edición, Springer. pp. 355-356.</li>
</ol>

ecuación de continuidad

La magnitud total de corriente que fluye por unidad de área transversal se llama densidad de corriente. Por lo tanto, la corriente que pasa a través de un área transversal se puede escribir como la integral de superficie de la densidad de corriente. <img alt="Equation1" src="/files/ftp_upload/14186/14186_Equation_1.png" style="text-align: center; height: 40px;"> De acuerdo con la conservación de la carga, la corriente total que fluye fuera de un volumen dado es igual a la tasa de disminución de carga dentro de ese volumen. <img alt="Equation2" src="/files/ftp_upload/14186/14186_Equation_2.png" style="text-align: center; height: 40px;"> Ahora, la carga total se puede escribir en términos de la densidad de carga volumétrica. <img alt="Equation3" src="/files/ftp_upload/14186/14186_Equation_3.png" style="text-align: center; height: 40px;"> La densidad de carga es una función espacial. Por lo tanto, aplicando la regla de Leibniz, la derivada temporal se puede mover dentro de la integral. <img alt="Equation4" src="/files/ftp_upload/14186/14186_Equation_4.png" style="text-align: center; height: 40px;"> Cuando se aplica el teorema de la divergencia al lado izquierdo de la ecuación anterior, la integral de superficie cerrada se convierte en la integral de volumen. <img alt="Equation5" src="/files/ftp_upload/14186/14186_Equation_5.png" style="text-align: center; height: 40px;"> Dado que esta relación se cumple para cualquier volumen, los integrandos son iguales y la relación obtenida se llama ecuación de continuidad. Esto establece que la divergencia de la densidad de corriente es igual a la tasa negativa de cambio de la densidad de carga volumétrica. <img alt="Equation6" src="/files/ftp_upload/14186/14186_Equation_6.png" style="text-align: center; height: 40px;"> Para corrientes estacionarias, la densidad de carga es invariante en el tiempo. Por lo tanto, la divergencia de la densidad de corriente es cero.

Ecuación de continuidad

La cantidad total de corriente que fluye por unidad de área de sección transversal se denomina densidad de corriente. Por lo tanto, la corriente que pasa a través de un área de sección transversal ...

Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

Current and Resistance

Corriente y resistencia

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

charge conservation and current flow

Charge conservation and current flow are linked through the continuity equation. The current density is the amount of current flowing per unit cross-sectional area. The current through a surface can be written as a surface integral of the current density.

The conservation of charge says that the total current leaving a volume equals the rate at which charge inside that volume decreases. The total charge can be written using volume charge density, which is a space function. Because of this, the time derivative can be moved inside the integral by applying the Leibniz rule.

Next, the divergence theorem is used on the left-hand side. This changes the closed surface integral into a volume integral. Since the relation must hold for any volume, the integrands must be equal. This gives the continuity equation, which states that the divergence of the current density equals the negative rate of change of volume charge density. For steady currents, the charge density does not change with time, so the divergence of the current density is zero.

Charge Conservation and Current Flow

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Charge conservation and current flow are linked through the continuity equation. The current density is the amount of current flowing per unit cross-sectional area. The current through a surface can be written as a surface integral of the current density. The conservation of charge says that the total current leaving a volume equals the rate at which charge inside that volume decreases. The total charge can be written using volume charge density, which is a space function. Because of this, the...

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Charge Conservation and Current Flow | JoVE K12

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Charge Conservation and Current Flow

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