Question

A magnetic field of $1T$ applied at an angle $\pi /3$ to the vertical direction is decreased to zero at a steady rate in one second. The magnitude of induced emf in a horizontally placed circular loop of radius $5cm$ is given by

• A. $1.25\sqrt{3}\pi mV$
• B. $1.25\sqrt{3}\pi V$
• C. $1.25\pi mV$
• D. $1.25\pi V$
• E. $25\pi V$

Answer 1

Answer: (C)

A magnetic field of $1T$ applied $\frac{\pi }{3}$ to the vertical direction is shown in figure below Induced Emf in circular ring.

$\epsilon =\frac{\Delta \varphi }{\Delta t}=\frac{BA\cos \theta }{t}$
$\Rightarrow \epsilon =\frac{1\times \pi {\left(5\times 10^{-2}\right)}^2\times \cos \frac{\pi }{3}}{1}$
$\Rightarrow \epsilon =1.25\pi mV$