Question

A circular loop of wire of radius $ 14\, \text{cm} $ is placed in a magnetic field directed perpendicular to the plane of the loop. If the field decreases steadily at a rate of $ 0.05\, \text{T/s} $, what is the magnitude of the induced emf in the loop?

• A. 2.08 mV
• B. 3.08 mV
• C. 2.16 mV
• D. 3.24 mV

Hint:

Use \( \text{emf} = A \cdot \frac{dB}{dt} \) when magnetic field is perpendicular to a circular loop.

Answer 1

The Correct Option is B

Faraday's Law: \[ \text{emf} = \left| \frac{d\Phi}{dt} \right| = A \cdot \left| \frac{dB}{dt} \right| \] Given: - Radius \( r = 14\, \text{cm} = 0.14\, \text{m} \)
- \( \frac{dB}{dt} = 0.05\, \text{T/s} \)
\[ A = \pi r^2 = \pi (0.14)^2 = \pi \cdot 0.0196 \approx 0.0616\, \text{m}^2 \] \[ \text{emf} = 0.0616 \cdot 0.05 = 3.08 \times 10^{-3}\, \text{V} = 3.08\, \text{mV} \]