Question

A solenoid has $1000$ turns, length of $30\text{cm}$ and an area of cross-section $1.5\times {10}^{-3}{\text{m}}^2.$ Near to its centre , a coaxial coil of $500$ turns is wounded. If a current changes through the solenoid at a rate of $8\text{A/s}$ , then find the emf induced in the coil.

• A. $67\text{mV}$
• B. $12.26\text{mV}$
• C. $83.45\text{mV}$
• D. $25.14\text{mV}$

Answer 1

The correct option is D $25.14\text{mV}$

From faraday's law, $e=\left|\begin{array}{c}\frac{d\varphi }{dt}\end{array}\right|=M\frac{di}{dt}$

$\Rightarrow e=\frac{{\mu }_0{N}_1{N}_{2}A}{l}\frac{di}{dt}$

Substituting the data given in the question gives,

$e=\frac{4\pi \times {10}^{-7}\times 5\times {10}^5\times 1.5\times {10}^{-3}\times 8}{0.3}=251.36\times {10}^{-4}\text{V}=25.14\text{mV}$

Hence, option $d$ is correct.