The induced emf can be produced in a coil by
A. moving the coil with uniform speed inside uniform magnetic field
B. moving the coil with non uniform speed inside uniform magnetic field
C. rotating the coil inside the uniform magnetic field
D. changing the area of the coil inside the uniform magnetic field
Choose the correct answer from the options given below:

Solution

Physics sir · 3 steps

For each case ask one thing: does the flux BA cos θ through the coil change? No change, no emf.

1. Faraday's law. An emf is induced only when the magnetic flux through the coil changes with time. For a flat coil in a uniform field, the flux depends on three things only.

   Φ = BA cos θ, ε = -dΦ/dt

   Statement	What changes?	Does Φ change?	Emf induced?
   A: moving with uniform speed	only the position; B, A, θ stay the same	no	no
   B: moving with non-uniform speed	only the position; B, A, θ stay the same	no	no
   C: rotating the coil	the angle θ	yes	yes
   D: changing the area	the area A	yes	yes

2. Why motion fails. In a uniform field, every position looks the same to the coil, so moving it, fast or slow, steady or not, leaves the flux constant. The motional emfs in opposite sides of the coil are equal and cancel around the loop.
3. So. Only rotating the coil (C) and changing its area (D) change the flux, so the answer is (b).

The idea to keep. In a uniform field, sliding a coil around never induces an emf, however its speed varies. Only a change in B, A or θ changes the flux, and only that gives an emf.

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