Question

An air-cored solenoid of length $0.3\text{m}$, area of cross section $1.2\times {10}^{-3}{\text{m}}^2$ has $2500\text{turns}$. Around its central section, a coil of $350\text{turns}$ is wound. The solenoid and the coil are electrically insulated from each other. The magnitude of EMF induced in the coil , if the initial current of $3\text{A}$ in the solenoid is reversed in $0.25\text{sec}$ is

• A. $0.2056\text{V}$
• B. $0.3056\text{V}$
• C. $0.1056\text{V}$
• D. $0.4056\text{V}$

Answer 1

The correct option is C $0.1056\text{V}$

$N_1=2500;N_2=350$

$A=1.2\times {10}^{-3}{\text{m}}^2;l=0.3\text{m}$

The mutual inductance , $M=\frac{{\mu }_0{N}_1{N}_{2}A}{l}$
$=\frac{4\pi \times {10}^{-7}\times 2500\times 350\times 1.2\times {10}^{-3}}{0.3}$

$=4.4\times {10}^{-3}\text{H}$

Induced EMF , $e=M\frac{dI}{dt}=4.4\times {10}^{-3}\times \frac{3-(-3)}{0.25}$

$=0.1056\text{V}$

Hence, option (c) is the correct answer.