Question

A square loop of side $10cm$ and resistance $0.5\Omega$ is placed vertically in the east-west plane. A uniform magnetic field of $0.10T$ is set up across the plane in the north-east diraction. The magetic field is decreased to zero in $0.70s$ at a steady rate. the magnitude of current in this time-interval is.

Answer 1

The initial magnetic flux is given as,

${\varphi }_i=BA\cos \theta$

${\varphi }_i=0.1\times {10}^{-2}\cos {45}^{\circ }$

${\varphi }_i=\frac{0.1\times {10}^{-2}}{\sqrt{2}}$

The final magnetic flux is given as,

${\varphi }_f=0$

The magnitude of induced emf is given as,

$e=\frac{\Delta \varphi }{\Delta t}$

$e=\frac{{10}^{-3}}{\sqrt{2}\times 0.7}$

$e=1.0mV$

The magnitude of the current is given as,

$I=\frac{e}{R}$

$I=\frac{1.0}{0.5}$

$I=2.0mA$