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Question

A conducting disc of radius r rotates with a small but constant angular velocity ω about its axis. A uniform magnetic field B exists parallel to the axis of rotation. Find the motional emf between the centre and the periphery of the disc.

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Solution

The angular velocity of the disc is ω. Also, the magnetic field of magnitude B is perpendicular to the disc.



Let us take a circular element of thickness da at a distance a from the centre.
Linear speed of the element at a from the centre, v = ωa
Now,
de=Blvde=B×da×aωe=0rBωada e=12Bωr2

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