The coil and magnet are moved in the same direction with same speed (V). The induced e.m.f. is

The coil and magnet are moved in the same direction with same speed (V). The induced e.m.f. is
  1. zero.
  2. proportional to V .
  3. proportional to $\mathrm{V}^{-1}$.
  4. finite but does not depend on V.

Solution

$e=-N \frac{d \phi}{d t}$
As the coil and magnet are moving in same direction in same speed, $\begin{array}{ll} \therefore & \phi=\mathrm{B} \cdot \mathrm{~A}=\mathrm{constant} \\ \therefore & \frac{\mathrm{~d} \phi}{\mathrm{dt}}=0 \end{array}$
Thus, the emf induced is zero because the relative speed of magnet with respect to coil is zero.

Asked in: MHT CET 2024 (02 May Shift 2)

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