First slide
Magnetic flux and induced emf
Question

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

Moderate
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 rod

ϕ=B12l2θcos0=12Bl2θ=12Bl2ωt And so e=dt=ddt12Bl2ωt=12Bl2ω

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