Current Density at Conductivity Boundaries

Current density at a boundary changes when two conducting materials have different electrical conductivities. The normal component of current density stays continuous across the interface. The tangential component, which runs along the surface, becomes discontinuous across the boundary.

Consider ...

The current density becomes discontinuous across an interface having different electrical conductivities.

For steady currents, the divergence of the current density is zero. So, the normal component of the current density is continuous across the boundary.

Recall that the tangential component of the electric field is continuous acr...