Solution:             Click For PDF Version

Two long parallel wires, each of radius a, whose centres are a distance d apart carry equal currents in opposite directions.

Let us calculate the flux of the magnetic field through the rectangular area ABCD .

We will find the magnetic field due to the two long current carrying wires. As the current is flowing in opposite directions, the magnetic field inside the rectangle ABCD will be perpendicular and into the plane of the figure (as shown in the figure).

The magnetic field at a distance r from a long wire carrying current is circular and its magnitude is

.

Therefore, the magnetic field due to both wires at a point a distance from the left-end wire will be

The flux through the rectangular area ABCD will therefore be given by the integral

Inductance is defined as the flux per unit current. Therefore, the inductance of the length l of the pairs of wires will be