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
.
![](Self Assesment_clip_image001.gif)
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
![](Self Assesment_clip_image002_0002.gif)
Thus the scalar potential is given by
![](Self Assesment_clip_image002_0003.gif)
Thus
![](Self Assesment_clip_image002_0004.gif)
This is a simple application of the magnetostatic boundary condition
![](Self Assesment_clip_image002_0005.gif)
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
![](Self Assesment_clip_image002_0007.gif)