A similar example is below. In your case use pi a^2 instead of Nab
and omega = 2 pi f
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A rectangular coil of N turns and of length a and width b is rotated at frequency f in a
uniform magnetic field B as indicated. The coil is connected to co rotating cylinders against
which metal brushes slide to make contact. (a) Show that the emf matches the given expression.
(b) What value of Nab gives an emf such that its maximum value is 150V. Take the angular
speed to be 60 rev/s and the field to be 0.5 T.
This is a classic induced emf problem. You are being asked to calculate the expression that
describes how a generator works.
We begin by writing out the flux for the loop in the configuration below (shown edge on).
q
B
ΦB = BAcosθ
= BNabcosθ
θ =ω t = 2π f t
ΦB = BAcos2π f t
Note that since the loop is rotating, we have substituted in for the angle in terms of the angular
velocity and then frequency. We can now find the induced emf
ΦB = B Nabcos2π f t
ε = − dΦB/d t
= 2π f BNabsin(2π f t)
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in your case
= omega B pi a^2 sin (omega t)
A circular loop of radius "a" is rotated at constant angular velocity ω in a uniform magnetic field B.
Find the magnitude of the net induced emf on the loop at any given time
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