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According to Faraday’s law, the total charge induced in a conductor that is moved in a magnetic field depends upon :

  • A.Change in magnetic flux
  • B.Initial magnetic flux
  • C.Final magnetic flux
  • D.Rate of change of magnetic flux

Answer: A

The total charge depends on the change in magnetic flux.

By Faraday's law the induced emf is the rate of change of flux. With circuit resistance R, the current is that emf over R, and the total charge is the current over the time of the change:

\[ \begin{aligned} q &= \int \frac{1}{R} \frac{d\Phi}{dt}\, dt \\ &= \frac{\Delta \Phi}{R} \end{aligned} \]

So the charge depends only on the total change in flux, not on how fast it happens. The rate of change decides the emf and current, which is the trap in the last option; the initial or final flux alone is not enough.

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