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

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