Rankers Physics
Topic: Electromagnetic Induction

15. The total charge, induced in a conducting loop when it is moved in magnetic field depend on (1992)

The rate of change of magnetic flux
Initial magnetic flux only
The total change in magnetic flux
Final magnetic flux only

Solution:

Induced charge $Q = \int I dt = \int \frac{e}{R} dt = \int \frac{1}{R} \frac{d\Phi}{dt} dt = \frac{\Delta \Phi}{R}$.
Thus, the total induced charge depends directly on the total change in magnetic flux, $\Delta \Phi$.
It is independent of the rate of change of flux or time.

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