Question

A solenoid of length 30 cm with 10 turns per centimetre and area of cross-Section 40 $c{m}^2$completely surrounds another co-axial solenoid of same length, area of Cross-section 20 $c{m}^2$ with 40 turns per centimetre. The mutual inductance of the

• A. 10 H
• B. 8 H
• C. 3mH
• D. 30 mH

Answer 1

The correct option is C 3mH

Given:

$n_1=10c{m}^{-1}=1000m^{-1}$
$n_2=40c{m}^{-1}=4000m^{-1}$
$l=30cm=30\times 10m^{-2}$
$A_2=20c{m}^2=20\times {10}^{-4}{m}^2$

Mutual inductance of the system,

$M={\mu }_0{n}_1{n}_2{A}_{2}l$ (Where $A_2$ is the area of inner solenoid.)

$\therefore M=4\pi \times {10}^{-7}\times 1000\times 4000\times 20\times {10}^{-4}\times 30\times {10}^{-2}$

$M=301.44\times {10}^{-5}H=3mH$