Question

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

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

Answer 1

The correct option is D $3.8\times {10}^{-6}$

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