The scalar magnetic potential, Vm , due to a current loop can be obtained by first dividin...

The scalar magnetic potential, Vm , due to a current loop can be obtained by first dividing the loop area into many small loops and then summing up the contribution of these small loops (magnetic dipoles); that is

where dm = anIds

Prove that

where Ω is the solid angle subtended by the loop surface at the field point P (see Figure).

Figure: Subdivided current loop for determination of scalar magnetic potential