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A rectangular coil lies in a region of uniform magnetic field B that is perpendicular to the plane of the coil. In which of the following situations will NO emf be induced in the coil?
- the magnetic field is increased uniformly
- the magnetic field is switched off
- the coil is rotated about the axis XX' (an in-plane axis)
- the coil is rotated about an axis perpendicular to the plane of the coil passing through its centre O
Correct answer: the coil is rotated about an axis perpendicular to the plane of the coil passing through its centre O
Solution
Induced emf requires a change in flux phi = B*A*cos(angle). Increasing or switching off B changes B and hence flux (emf induced). Rotating about an in-plane axis XX' changes the angle between the area vector and B, so flux changes (emf induced). But rotating about the axis perpendicular to the coil's plane keeps the area vector parallel to B and the enclosed area unchanged, so flux is constant and no emf is induced.
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