Q: A solenoid is of length 50 cm and has a radius of 2 cm. It has 500 turns. Around its central section a coil of 50 turns is wound. Calculate the mutual inductance of the system.
Sol: NP = 500, NS = 50 ; A = π × 0.02 × 0.02 m2
μ0 = 4π× 10-7 Hm-1, l = 50 cm = 0.5 m
$\large M = \frac{\mu_0 N_p N_s A}{l} $
$\large M = \frac{4\pi \times 10^{-7} \times 500 \times 50 \times \pi (0.02)^2}{0.5} $
=789.8 × 10-7 H = 78.98 μH.