A circular coil of radius 10 cm has 500 turns. A magnetic field which is directed perpendicular to its plane is increasing at a rate of 0.5 T/s. If the resistance of the coil is 5 Ω. Find the current induced in the coil.

1.57 A

The correct answer is Option (1) - 1.57 A

Faraday law states that the induced EMF in a coil is given by -

$EMF=-N\frac{d\phi_B}{dt}$

where,

N, number of turns in coil = 500

$\phi_B$, magnetic flux

$\frac{d\phi_B}{dt}$, Rate of change of magnetic flux

Also, $\phi_B=\vec B.\vec A$

and,

$\vec A$ = Area of coil = $\pi r^2=\pi(0.1)^2$

$=0.0314m^2$

$∴\frac{d\phi_B}{dt}=A\frac{dB}{dt}$

$\frac{d\phi_B}{dt}=0.0314×0.5=0.0157\,Tm^2/s$

Hence,

$EMF=-N\frac{d\phi_B}{dt}=-500×0.0157$

$=-7.85V$

∴ Current = $\frac{emf}{R}$ [By ohm's law]

$=\frac{-7.85}{5}=1.57A$