Question

A small circular loop, of radius 3cm, and a bigger loop, of radius 20cm, are placed coaxially, at a distance of 15cm as shown in the figure. A current of 2A flows through the smaller loop. Find the flux linked with the bigger loop and the mutual inductance of the two loops.

Answer 1

By symmetry, the flux linked with the bigger loop, due to current in the smaller loop, will be same as the flux linked with the smaller loop, due to the same current in the bigger loop 

(∴ M₁₂ = M₂₁ = M). 

Now the magnetic field, at the centre of smaller loop, due the to a current, i, in the bigger loop, is

The field B, is along the axis. The flux linkage, with the smaller loop due to B₁ this field will be (nearly)

This is the same as the flux ϕ₁ , linked with the bigger coil, due to same current in the smaller loop. We, therefore, have