26.11:

Boundary Conditions for Current Density

JoVE Core
Physique
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JoVE Core Physique
Boundary Conditions for Current Density

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01:25 min

September 18, 2023

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.

Equation1

However, the tangential components of the current density are discontinuous across the interface.

Equation2

Consider an interface separated by two conducting media with conductivities σ1 and σ2. The steady current density at the interface is , in medium 1 at a point P1. It makes an angle α1 with the normal. The current density  at point P2 in medium 2 makes an angle α2 with the normal.

Figure1

The normal and tangential components of the current density give the equations as follows:

Equation3

Equation4

Taking the ratio of the two equations, the expression for the electrical conductivities in both the media is obtained.

Equation5

If the electrical conductivity of medium 1 is greater than that of medium 2, the angle α2 approaches zero. This implies that the current density  is normal to the surface of conductor 1.