Question

A long solenoid with $10$ turns per cm has a small loop of area $3c{m}^2$ placed inside, normal to the axis of the solenoid. If the current carried by the solenoid changes steadily from $2A$ to $4A$ in $0.2s$, what is the induced voltage in the loop, while the current is changing?

• A. $4.2\times 10^{-8}V$
• B. $2.8\times 10^{-8}V$
• C. $7.3\times 10^{-6}V$
• D. $3.8\times 10^{-6}V$

Answer 1

Answer: (D)

Here, $\frac{N}{l}=10$ turns per $cm=1000$ turns per $m$
$A=3c{m}^2=3\times 10^{-4}{m}^2$ or $\frac{dl}{dt}=\frac{4-2}{0.2}=10A{s}^{-1}$
Also $\epsilon =\frac{d\varphi }{dt}=\frac{d}{dt}\left(BA\right)=A\frac{d}{dt}\left({\mu }_0\frac{N}{t}I\right)<br>=A{\mu }_0\left(\frac{N}{l}\right)\frac{dI}{dt}$
$=3\times 10^{-4}\times 4\pi \times 10^{-7}\times 1000\times 10$
$=3.8\times 10^{-6}V$