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Which of the following statements about a variable (time-changing) magnetic flux is correct?

1. It can change sinusoidally with time
2. It must always be increasing
3. It must become zero at the instant the induced field is maximum
4. None of these

Correct answer: It can change sinusoidally with time

Solution

A time-varying flux is not required to increase monotonically; it can vary in any way, including sinusoidally (as in an AC generator). The induced emf is proportional to -d(phi)/dt; when phi = phi0*sin(omega*t) the induced quantity peaks where the flux is zero (max slope), which is the opposite of option 3's general claim. So the only correct general statement is that the flux can change sinusoidally.

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