Question

A small coil of radius r is placed at the centre of a large coil of radius R, where R >> r. The two coils are coplanar. The mutual induction between the coils is proportional to 

(a) r/R 

(b) r²/R 

(c) r^2/R² 

(d) r/R²

Answer 1

Correct Answer is: (b) r²/R 

Let I current flow in the larger coil.

Magnetic field at the centre = B = μ₀I/2R.

Flux linked with the smaller coil = ϕ = πr²B (πr²) μ₀I/2R.

But, ϕ = MI 

or M ϕ/I = (μ₀π/2) r²/R.