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Question
A metal disc of radius 30 cm spins at 20 revolution per second about its transverse symmetry axis in a uniform magnetic field of 0.20 T. The field is parallel to the axis of rotation. Calculate
(a) the area swept out per second by the radius of the disc
(b) the flux cut per second by a radius of the disc
(c) the induced emf between the axle and rim of the disc.
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Solution
Data: R = 0.3 m, f = 20 rps, B = 0.2 T
(a) The area swept out per unit time by a given radius = (the frequency of rotations) x (the area swept out per rotation) = f(πr2)
= (20)(3.142 × 0.09) = 5.656 m2
(b) The time rate at which a given radius cuts magnetic flux
`= ("d"phi_"m")/("dt") = "B f"(pi"r"^2)`
= (0.2)(5.656) = 1.131 Wb/s
(c) The magnitude of the induced emf,
`|e| = ("d"phi_"m")/"dt"` = 1.131 V
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