Question

A loop moves towards a stationary magnet at constant speed \(V\), resulting in an induced emf \(E\) within the loop. If the magnet also moves away from the loop at the same speed \(V\), the new induced emf in the loop is

• A. \(E\)
• B. \(\dfrac{E}{2}\)
• C. \(2E\)
• D. \(0\) \bigskip

Hint:

Induced emf depends on the rate of change of magnetic flux, not on the individual motions of the magnet or loop. If the relative position between the magnet and loop remains unchanged, \[ \frac{d\Phi}{dt}=0 \] and hence no emf is induced.

Answer 1

The Correct Option is D

Concept: Induced emf depends on relative motion. If loop and magnet move together with same speed, relative velocity = 0, flux constant, emf = 0.

Step 1: Relative speed = \(V - V = 0\). Flux constant \(\Rightarrow d\Phi/dt = 0 \Rightarrow \mathcal{E} = 0\).

Step 2: Write the final answer. \(\boxed{\mathcal{E}=0}\)