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Problem 4 - Olympiad

A copper disc of radius R rotates with angular velocity ω in a uniform magnetic field B perpendicular to its plane. A potential difference develops between the axis and the rim of the disc. What is the magnitude of this potential difference?

Correct: A

This is a case of motional EMF in a rotating disc. Each radial element of the disc moves perpendicular to the magnetic field. The EMF is given by integrating dE = Bvdr from 0 to R. Since v = ωr, we get E = ∫₀ᴿ Bωr dr = ½BωR². The potential difference between axis and rim is this value.