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. (c) the total change in magnetic flux. (d) the rate of change of magnetic flux.

Answer: (c). q = ∫ I dt = ∫ 1/R(dφ)/(dt)dt = (Δφ)/(R) The time taken cancels, so q depends only on the total change in flux (for a given R), not on its rate. So the answer is (c) the total change in magnetic flux.

The total charge induced in a conducting loop when it is moved in a… | MHT CET 2025 (22 Apr, Shift 1)

Q29MHT CET 2025 · 22 APR · SHIFT 1Easy

Magnetic Flux & Faraday's Law

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

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Answer: (c)

$q = \int I\,dt = \int \frac{1}{R}\frac{d\phi}{dt}dt = \frac{\Delta\phi}{R}$
The time taken cancels, so $q$ depends only on the total change in flux (for a given $R$ ), not on its rate.
So the answer is (c) the total change in magnetic flux.

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