Question

A 2 m long solenoid with diameter 2 cm and 2000 turns has a secondary coil of 1000 turns wound closely near its midpoint. The mutual inductance between the two coils is

• A. 2.4 x 10-4 H
• B. 3.9 x 10-4 H
• C. 1.28 x 10-3 H
• D. 3.14 x 10-3 H

Answer 1

Answer: (B)

3.9 x 10-4 H

Answer 2

Here l = 2 m, diameter = 2 cm

$\therefore$ radius , $r = \frac{2}{2} = 1cm = 1 \times 10^{- 2}m$

$N_{1} = 2000,N_{2} = 1000$

Area $= \pi r^{2} = \pi \times (1 \times 10^{- 2})^{2}$

Mutual inductance , $M = \frac{\mu_{0}N_{1}N_{2}A}{l}$

$= \frac{4\pi \times 10^{- 7} \times 2000 \times 1000 \times 3.14 \times 10^{- 4}}{2}$

$= 3.9 \times 10^{- 4}H$