Question

An air-cored solenoid with length 30 cm, area of cross-section $25c{m}^2$ and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of ${10}^{-3}s$. How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.

Answer 1

$B=\frac{{\mu }_{0}NI}{l}$
(Inside the solenoid away from the ends)
$\Phi =\frac{{\mu }_{0}NI}{l}A$
Total flux linkage = $N\varphi$
$=\frac{{\mu }_0{N}^{2}A}{l}I$
(Ignoring end variations in B)
$|\epsilon |=\frac{d}{dt}\left(N\Phi \right)$
$|\epsilon {|}_{av}=\frac{totalchangeinflux}{totaltime}$
$|\epsilon {|}_{av}=\frac{4\pi \times {10}^{-7}\times 25\times {10}^{-4}}{0.3\times {10}^{-3}}\times (500{)}^2\times 2.5$
$=6.5V$