Question

A circular coil of wire consists of exactly $100$ turns with a total resistance $0.20\Omega$. The area of the coil is $100$ ${cm}^2$. The coil is kept in a uniform magnetic field $B$ as shown in figure. The magnetic field is increased at a constant rate of $2T$ $s^{-1}$. If the induced current in the coil is ($x+495$)A, find the value of $x$.

Answer 1

Magnetic Flux:
$\varphi =N\int \overrightarrow{B}.d\overrightarrow{A}=NBAcos\left(60\right)=\frac{NBA}{2}$

Faraday's law:
$E=\frac{d\varphi }{dt}=N\frac{A}{2}\frac{dB}{dt}=100V$

By Ohm's Law:
$I=\frac{V}{R}=\frac{100}{0.2}=500A$

Hence, $x=5$