A constant magnetic field of 1T is applied in the x > 0 region. A metallic circular ring of radius 1m is moving with a constant velocity of 1 m/s along the x-axis. At t = 0s, the centre of O of the ring is at x = -1m. What will be the value of the induced emf in the ring at t = 1s? (Assume the velocity of the ring does not change.)

Solution

Physics sir · 3 steps

At t = 1 s the centre sits on the boundary, so the cutting length is the full diameter, 2 m.

1. Where the ring is. The centre starts at x = -1 m and moves at 1 m s⁻¹. At t = 1 s it is at x = 0, so exactly half the ring is inside the field.
2. Rate of flux change. EMF comes from the field area growing as the ring slides in. New area enters through the chord lying on the line x = 0. When the centre is on that line, the chord is the diameter, L = 2R = 2 m.

   ε = B dA/dt = B L v = 1 × 2 × 1 = 2 V

3. So. The induced emf at t = 1 s is 2 V, option (c).

The idea to keep. For a loop entering a field, use ε = BLv with L as the length of the loop cut by the field boundary at that instant, not the loop's full size.

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