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Q.

A copper rod of length l is rotated about one end perpendicular to the magnetic field B with constant angular velocity  ω. The induced e.m.f. between the two ends is

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a

12Bωl2

b

34Bωl2

c

Bωl2

d

2Bωl2

answer is A.

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Detailed Solution

If in time t. the rod turns by an angle θ, the area generated by the rotation of rod will be  =12l×lθ So the flux linked with the area generated by the rotation of rodϕ=B12l2θcos⁡0=12Bl2θ=12Bl2ωt And so e=dϕdt=ddt12Bl2ωt=12Bl2ω
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A copper rod of length l is rotated about one end perpendicular to the magnetic field B with constant angular velocity  ω. The induced e.m.f. between the two ends is