Question

Mutual inductance M between two concentric coil of radius 1 centimetre and 2 metre is?​

Answer 1

answer : $\frac{\mu_0\pi}{4}$

explanation : let's derive the formula, after that you can easily find the mutual inductance M.

Let two concentric circular coils of radii r and R are given where r < R.

a current I2 flows through the outer circular coil.

so, magnetic field at the centre of circular coil, $B_2=\frac{\mu_0I_2}{2R}$

magnetic field B2 may be considered as constant over the cross sectional area of the inner smaller coil.

now, magnetic flux through inner coil, Φ1 = B2A1

or, MI2 = B2.A1

or, MI2 = $\frac{\mu_0I_2}{2R}$ × πr²

or, M = $\frac{\mu_0\pi r^2}{2R}$

here, r = 1cm = 1m , R = 2m

so, M = $\frac{\mu_0\pi(1)^2}{2(2)}$

= $\frac{\mu_0\pi}{4}$