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A square loop of side a and resistance R is moved through a distance x with velocity v inside a region of uniform magnetic field B, the loop remaining entirely within the field throughout. Find the work done in moving the loop.

1. 0
2. B² a² v x / R
3. 2 B² a² v x / R
4. 4 B² a² v x / R

Correct answer: 0

Solution

While the square loop is completely inside a uniform magnetic field, the magnetic flux through it does not change as it moves (same area, same field). With no change in flux, there is no induced emf, hence no induced current and no opposing magnetic force. Therefore no work is required to move the loop (against electromagnetic induction); the work done is zero.

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