At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5s, then induced EMF in the loop is :

Solution

Physics sir · 3 steps

Cut the two triangular notches out of the rectangle, then multiply that area by dB/dt.

1. Area of the loop. Start with the full rectangle: 16 × 4 = 64 cm². Each side notch is a triangle with base 4 cm and height 2 cm, so its area is 1/2 × 4 × 2 = 4 cm². Removing both leaves 64 - 8 = 56 cm² = 56 × 10⁻⁴ m².
2. Rate of change. Use 1 G = 10⁻⁴ T. The field falls by 500 G = 0.05 T in 5 s, so dB/dt = 0.01 T s⁻¹. It stays constant because the drop is linear.

   ε = AdB/dt = (56 × 10⁻⁴ m²)×(0.01 T s⁻¹) = 56 × 10⁻⁶ V

3. So. The induced EMF is 56 μV, option (c).

The idea to keep. With the loop fixed and B changing, the EMF is the area times dB/dt. Get the area right first, and convert gauss to tesla using 1 G = 10⁻⁴ T.

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