Iniciar sesión

The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area can be written as the surface integral of the current density.

Equation1

According to the conservation of charge, the total current flowing out of a given volume equals the rate of decrease of charge within that volume.

Equation2

Now, the total charge can be written in terms of the volume charge density.

Equation3

The charge density is a space function. Hence, applying the Leibniz rule, the time derivative can be moved inside the integral.

Equation4

When the divergence theorem is applied to the left-hand side of the above equation, the closed surface integral is converted into the volume integral.

Equation5

Since this relation holds for any volume, the integrands are equal and the obtained relation is called the continuity equation. This states that the divergence of the current density equals the negative rate of change of volume charge density.

Equation6

For steady currents, the charge density is invariant with time. Hence, the divergence of the current density is zero.

Tags
Continuity EquationCurrent DensityCharge ConservationSurface IntegralVolume Charge DensityLeibniz RuleDivergence TheoremVolume IntegralSteady CurrentsNegative Rate Of Change

Del capítulo 26:

article

Now Playing

26.10 : Continuity Equation

Current and Resistance

695 Vistas

article

26.1 : Corriente eléctrica

Current and Resistance

5.2K Vistas

article

26.2 : Velocidad de deriva

Current and Resistance

3.7K Vistas

article

26.3 : Densidad de corriente

Current and Resistance

3.6K Vistas

article

26.4 : Resistividad

Current and Resistance

3.2K Vistas

article

26.5 : Resistencia

Current and Resistance

4.0K Vistas

article

26.6 : Ley de Ohm

Current and Resistance

5.1K Vistas

article

26.7 : Dispositivos no óhmicos

Current and Resistance

962 Vistas

article

26.8 : Energía eléctrica

Current and Resistance

2.9K Vistas

article

26.9 : Energía eléctrica

Current and Resistance

1.1K Vistas

article

26.11 : Condiciones de contorno para la densidad de corriente

Current and Resistance

712 Vistas

article

26.12 : Conductividad eléctrica

Current and Resistance

992 Vistas

article

26.13 : Teoría de la Conducción Metálica

Current and Resistance

1.2K Vistas

JoVE Logo

Privacidad

Condiciones de uso

Políticas

Investigación

Educación

ACERCA DE JoVE

Copyright © 2025 MyJoVE Corporation. Todos los derechos reservados