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Question:

A metallic rod of length 'l' is tied to a string of length 2l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. induced across the ends of the rod is:

5Bωl²/2

2Bωl²/2

3Bωl²/2

4Bωl²/2

Solution:

de=B(ωx)⋅dxe=Bω∫₀²ˡ x⋅dx=5BωL²/2