Magnetic potential

In physics, the magnetic potential is a method of representing the magnetic field by using a potential value instead of the actual mathbf{B} vector field. There are two methods of relating the magnetic field to a potential field and they give rise to two possible types of magnetic potential.

Magnetic scalar potential

The magnetic scalar potential is defined by the equation:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:mathbf{H} = - abla mathbf{psi}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Applying Ampere's Law to the above definition we get:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

: abla imes mathbf{H} = - abla imes abla mathbf{psi} = mathbf{J}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Since in any continuous field, the curl of a gradient is zero, this would suggest that magnetic scalar potential fields cannot support any sources. In fact, sources can be supported by applying discontinuities to the potential field (thus the same point can have two values for points along the disconuity). These discontinuities are also known as "cuts". When solving magnetostatics problems using magnetic scalar potential, the source currents must be applied at the discontinuity.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~