Question

A conducting circular loop of radius $\frac{10}{\sqrt{\pi}} cm$ is placed perpendicular to a uniform magnetic field of $0.5 T$ The magnetic field is decreased to zero in $0.5 s$ at a steady rate The induced emf in the circular loop at $0.25 s$ is:

• A. $emf =1 mV$
• B. $emf =100 mV$
• C. $emf =5 mV$
• D. $emf =10 mV$

Answer 1

The Correct Option is D

The area of the loop is: \[ A = \pi r^2 = \pi \left(\frac{10}{\sqrt{\pi}}\right)^2 = 100 \, \text{cm}^2 = 10^{-2} \, \text{m}^2. \] The magnetic flux through the loop is: \[ \Phi = B \cdot A = 0.5 \cdot 10^{-2} = 5 \cdot 10^{-3} \, \text{Wb}. \] The emf induced is: \[ \mathcal{E} = \left| \frac{\Delta \Phi}{\Delta t} \right| = \frac{5 \cdot 10^{-3}}{0.5} = 10 \, \text{mV}. \]