1. Calculate the magnetic scalar potential at a distance z from a circular current loop of radius a and hence calculate the magnetic field at that point.

The problem is essentially to calculate the solid angle subtended by the current loop at a distance z from its centre.  With the point where we need the scalar potential as the centre draw a sphere of radius .

 

It is easy to show that the part of the sphere above the loop has an area . Since an area  subtends a solid angle , the loop subtends .  In terms of the distance z from the centre of the loop, the solid angle is

Thus the scalar potential is given by

Thus

2. A current sheet of    (in kA/m) separates two regions of space at z=0. The magnetic field   in region 1 (z>0) is given by  (in mT) exists. If both regions are non-magnetic, determine the field in region 2 (z<0).

This  is a simple application of the magnetostatic boundary condition

In this case,  so that,   (kA/m).  Multiplying with  H/m , we get  mT. Thus  the magnetic field of induction in the second medium is