Question

A conducting square loop having edges of length 2.0 cm is rotated through ${180}^{\circ }$ about a diagonal in 0.20 a. A magnetic field B exists in the region which is perpendicular to the loop in its initial position. If the average induced emf during the rotation is 20 mV, find the magnitude of the magnetic field.

Answer 1

Here e =20 mV $=20\times {10}^{-3}V$

$A=(2\times {10}^{-2}{)}^2=4\times {10}^{-4}$

dt =0.2 s,

$\varphi ={180}^{\circ },{\varphi }_1=2BA$

$e=\frac{d\varphi }{dt}=\frac{2BA}{dt}$

$\Rightarrow 20\times {10}^{-3}=\frac{2\times B\times 4\times {10}^{-4}}{2\times {10}^{-1}}$

$\Rightarrow 20\times {10}^{-3}=4\times B\times {10}^{-3}$

$\Rightarrow B=\frac{20\times {10}^{-3}}{4\times {10}^{-3}}=5T$