A conducting circular loop of radius 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.
- B.
- C.
- D.
Show answer and solution
Correct option: B
Solution
The EMF = -dΦ/dt = A × |dB/dt|.
Area A = π × (10/√π × 10⁻²)² = π × (100/π) × 10⁻⁴ = 10⁻² m².
Rate of change of B = 0.5/0.5 = 1 T/s (steady/constant rate).
EMF = A × (dB/dt) = 10⁻² × 1 = 10⁻² V = 10 mV.
Since the rate is constant, the induced EMF is the same at every instant including t = 0.25 s.
Area A = π × (10/√π × 10⁻²)² = π × (100/π) × 10⁻⁴ = 10⁻² m².
Rate of change of B = 0.5/0.5 = 1 T/s (steady/constant rate).
EMF = A × (dB/dt) = 10⁻² × 1 = 10⁻² V = 10 mV.
Since the rate is constant, the induced EMF is the same at every instant including t = 0.25 s.
[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]