We have to show that B at the centre of a rectangular loop of wire of length L and width W, carrying a current , is given by

Solution:             Click For PDF Version

We first calculate the magnetic field due to a straight wire segment of length l, carrying current , at a distance r from its mid-point.

Using Biot-Savart law we write the expression for the magnetic field at P due to an infinitesimal current element .

In the integral, we make the substitution

We get

We will use this result and write contributions to at P due to the current carrying line segments , , and .