What is surface current density

Surface current density refers to the amount of electric current flowing per unit length along a surface. It is a vector quantity that describes how the current is distributed across a specific surface area, often in the context of conductive materials, such as metals or thin films.

Mathematically, surface current density $mathbf{K}$ is expressed as:

Where:

• $I$ is the total current flowing along the surface.

• $L$ is the length of the conducting surface along which the current is flowing.

Alternatively, it can be expressed in terms of the electric field and the conductivity of the material:

Where:

• $sigma$ is the electrical conductivity of the material.

• $mathbf{E}$ is the electric field at the surface.

Surface current density is especially relevant in scenarios involving thin conductors, such as microelectronics or when studying the behavior of currents near surfaces like the boundary of a conductor or a semiconductor.

This concept also plays a key role in understanding phenomena like the skin effect, where current tends to flow mostly near the surface of a conductor at high frequencies.