Question

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

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

Answer 1

The correct option is B $4V$

Given:

$l=20cm=20\times {10}^{-2}m$

$A=20c{m}^2=20\times {10}^{-4}{m}^2$

$N=400,$

$I_1=2A,I_2=0,dt={10}^{-3}s$

$ϵ=\frac{d\varphi }{dt}=\frac{d\left(BAN\right)}{dt}$

$=\frac{{\mu }_{0}NdIAN}{ldt}$

$=\frac{{\mu }_{0}N(I_1-I_2)AN}{ldt}$

$=\frac{d\varphi }{dt}=\frac{d\left(BAN\right)}{dt}$

$ϵ=\frac{4\pi \times {10}^{-7}\times (400{)}^2\times 2\times \times {10}^{-4}}{20\times {10}^{-2}\times {10}^{-3}}$

$ϵ=4$V