Let a small element dy in the loop at a distance of y as shown in the given figure:

Magnetic field associated with the the element taken i.e. dy can be calculated as follows:

dФ = BdA ………………..(i)

where dA is the area of the element dy i.e. ady

B is the magnetic field intensity of the element dy at a distance of y and can be written as:

Putting in the equation (i)

Putting limits of y from x to a + x

Mutual conductance is given by the relation:

Ф = MI

Where MI =

Or M =