A conducting circular loop of radius 10/√π 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 :

Solution

Physics sir · 3 steps

Steady fall in B means a constant emf, so the 0.25 s is a distractor. Just find area times dB/dt.

1. Area of loop. r = 10/√π cm, so A = π r² = π × 100/π = 100 cm² = 0.01 m².
2. Rate of change. The field falls from 0.5 T to zero in 0.5 s at a steady rate, so |dB/dt| = 0.5/0.5 = 1 T s⁻¹ at every instant, including t = 0.25 s.

   |ε| = A|dB/dt| = 0.01 × 1 = 0.01 V

3. So. The induced emf is 0.01 V = 10 mV, the same at 0.25 s as at any other moment of the decrease. The answer is (a).

The idea to keep. Induced emf depends on how fast the flux changes, not on how much flux is left. If B changes at a steady rate, the emf is constant for the whole interval.

Answer from the NTA final answer key. Solution by PrepWiser.