A square loop of side 15 cm being moved towards right at a constant speed of 2 cm / s as shown in figure. The front edge enters the 50 cm wide magnetic field at t=0. The value of induced emf in the loop at t=10 s will be :

Solution

Physics sir · 3 steps

First find where the loop is at t = 10 s: it sits wholly inside the field, so the flux stops changing.

1. Locate the loop. In 10 s at 2 cm s⁻¹ the loop moves 20 cm. The front edge is now 20 cm inside the field, and the back edge is 20 - 15 = 5 cm inside.
2. Check the timeline. The back edge enters at t = 15/2 = 7.5 s. The front edge reaches the far boundary only at t = 50/2 = 25 s. So from 7.5 s to 25 s the whole loop is inside the field, and t = 10 s falls in that window.

   ε = -dΦ/dt = -d/dt(B × l²) = 0

3. So. With the loop fully inside a uniform field, the flux stays fixed at B l². The emfs Bvl in the front and back edges are equal and cancel around the loop, so the induced emf is zero, option (a).

The idea to keep. A loop gets an emf only while its flux changes, that is while it is entering or leaving the field. Always find the loop's position at the given time before using Bvl.

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