Q112 / 150 · MHT CET 2025 (22 Apr Shift 1) · Physics

The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on

  • A
    initial magnetic flux only.
  • B
    final magnetic flux only.
  • Correct answer
    C
    the total change in magnetic flux.
  • D
    the rate of change of magnetic flux.

Solution

The induced charge in a conducting loop is determined by Faraday's law and Ohm's law. The induced electromotive force $E = -\frac{d\Phi}{dt}$ drives a current $I = \frac{E}{R} = -\frac{1}{R}\frac{d\Phi}{dt}$ through the loop.

Integrating this current over time gives the total charge: $q = \int I dt = -\frac{1}{R} \int d\Phi = -\frac{1}{R}(\Phi_f - \Phi_i)$.

Hence $|q| = \frac{|\Delta\Phi|}{R}$, showing that the total induced charge depends only on the net change in magnetic flux and the loop's resistance.

Final answer: $\boxed{C}$

Hence, the correct answer is option: 'C'.

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