A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf (ε) with time (t) is given by

Solution

Physics sir · 4 steps

Only one side of the loop is still cutting field lines, at a fixed speed, so the emf stays fixed.

1. Flux inside. Let l be the side of the loop that lies along the field boundary, and let x be the length still inside the field. The flux through the loop is Φ = Blx.
2. Rate of change. The loop moves out at constant speed v, so x shrinks at the steady rate |dx/dt| = v. The flux falls linearly with time.

   |ε| = |dΦ/dt| = Bl|dx/dt| = Blv

3. Same picture. Equivalently, only the side of length l still inside the field cuts field lines. Its motional emf is Blv. Here B, l and v are all constant, so ε does not change with t.
4. So. While the loop is partly inside the field, the graph of ε against t is a horizontal line. That is option (b).

The idea to keep. Emf depends on how fast the flux changes, not on how much flux is left. If the area in the field changes at a steady rate, the emf Blv stays constant.

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