Question

A long solenoid with $10$ turns per cm has a small loop of area $3\, cm^{2}$ placed inside, normal to the axis of the solenoid. If the current carried by the solenoid changes steadily from $2\, A$ to $4\, A$ in $0.2\, s$, 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 $m$
$A=3\,cm^{2}=3\times 10^{-4}\,m^{2}$ or $\frac{dl}{dt}=\frac{4-2}{0.2}=10\,A\, s^{-1}$
Also $\varepsilon=\frac{d\phi}{dt}=\frac{d}{dt}\left(BA\right)=A \frac{d}{dt} \left(\mu_{0}\frac{N}{t}I\right)
=A\,\mu_{0}\left(\frac{N}{l}\right) \frac{dI}{dt}$
$=3\times10^{-4}\times4\,\pi\times10^{-7}\times1000\times10$
$=3.8\times10^{-6}\,V$