Question

A solenoid has a cross sectional area of $6.0\times {10}^{-4}{m}^2$, consists of 400 turns per meter, and carries a current 0.4 A and are connected to a circumference of the solenoid. The ends of the coil are connected to a 1.5$\Omega$ resistor. Suddenly, a switch is opened, and the current in the solenoid dies to zero in a time 0.050 s. Find the average current passing through the coil during this time.

Answer 1

$\epsilon =\frac{-d\varphi }{dt}$

for $N$ no. of turns,

$\epsilon =-N\frac{d\varphi }{dt}$

$=-N\frac{d\left(BA\cos \right(0\left)\right)}{dt}=-NA\frac{dB}{dt}$

$I=-\frac{N\frac{dB}{dt}A}{R}=-\frac{NA\frac{{\mu }_{0}n\Delta I}{dt}}{R}$

$=\frac{\left(10\right)(6\times {10}^{-4})\frac{(4\pi \times {10}^{-7})\left(400\right)\left(0.4\right)}{0.050}}{1.5\Omega }$

$I=1.6\times {10}^{-5}A$