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.
Answer & explanation
Correct answer: option 1
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]
$=\frac{-7.85}{5}=1.57A$