Magnetic Potential - Magnetic Scalar Potential

Magnetic Scalar Potential

The scalar potential is another useful quantity in describing the magnetic field, especially for permanent magnets.

In a simply connected domain where there is no free current,

hence we can define magnetic scalar potential ψ as

Using the definition of H:

it follows that

Here ∇ • M acts as the source for magnetic field, much like ∇ • P as the source for electric field. So analogously to bound electric charge, the quantity

is called the bound magnetic charge.

If there is free current, one may subtract the contribution of free current per Biot-Savart law from total magnetic field and solve the remainder with the scalar potential method.