Question

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

• A. $2.4\times {10}^{-4}$ H
• B. $3.9\times {10}^{-4}$ H
• C. $1.28\times {10}^{-3}$ H
• D. $3.14\times {10}^{-3}$ H

Answer 1

The correct option is B $3.9\times {10}^{-4}$ H

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

$N_1$ = 2000, $N_2$ = 1000

Area = $\pi r^2$ = $\pi \times {(1\times {10}^{-2})}^2=3.14\times {10}^{-4}{m}^2$

Mutual inductance, M = $\frac{{\mu }_0{N}_1{N}_{2}A}{l}$

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

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