Question

An air cored solenoid with length $20\, cm$, area of cross section $20\, cm^{2}$ and number of turns $400$ carries a current $2\, A$. The current is suddenly switched off within $10^{-3}\, s$. The average back emf induced across the ends of the open switch in the circuit is (ignore the variation in magnetic field near the ends of the solenoid)

• A. $2\,V$
• B. $4\,V$
• C. $3\,V$
• D. $5\,V$

Answer 1

Answer: (B)

Here, $l = 20\, cm = 20 \times 10^{-2}\, m$,
$A=20\,cm^{2}=20\times10^{-4}\,m^{2}$
$N=400$, $I_{1}=2\,A$, $I_{2}=0$, $dt=10^{-3}\,s$
As $\varepsilon= \frac{d \,\phi}{dt}=\frac{d(BAN)}{dt}$
$=\frac{\mu_{0}N\,dl\,AN}{l\,dt}\left(\because B=\frac{\mu_{0}NI}{t}\right)$
$=\frac{\mu_{0}N (I_{1}-I_{2})AN}{l\,dt}$
$=\frac{ 4\,\pi\times10^{-7}\times(400)^{2}\times2\times20\times10^{-4}}{20\times10^{2}\times10^{-3} }$
$=4\, V$