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A long, straight current-carrying wire lies along a diameter of a circular conducting loop, without touching it. Which statement(s) is/are correct?

1. the emf induced in the loop is zero if the current is constant
2. the emf induced in the loop is infinite if the current is constant
3. the emf induced in the loop is zero if the current decreases at a steady rate
4. the emf induced in the loop is finite if the current decreases at a steady rate

Correct answer: the emf induced in the loop is zero if the current decreases at a steady rate

Solution

Because the wire lies along a diameter, the magnetic flux it produces through one half of the loop is exactly cancelled by the equal and opposite flux through the other half. Net flux = 0 always, so the induced emf = -d(flux)/dt = 0 whether the current is constant or changing (including steadily decreasing). The statement that emf is zero when the current decreases at a steady rate is therefore correct (and likewise it is zero for constant current).

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