Question

A magnetic field of $1\, T$ 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 $5\, cm$ 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 $1\, T$ applied $\frac{\pi}{3}$ to the vertical direction is shown in figure below Induced Emf in circular ring.

$ \varepsilon=\frac{\Delta \phi}{\Delta t}=\frac{B A \cos \theta}{t} $
$\Rightarrow \varepsilon=\frac{1 \times \pi\left(5 \times 10^{-2}\right)^{2} \times \cos \frac{\pi}{3}}{1} $
$ \Rightarrow \varepsilon =1.25 \,\pi \,mV $