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Calculating the Potential Difference

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Question: Consider a generator constructed as shown in the attachment. The loop in this generator rotates at an angular rate of w. The slip rings in this design ensure that the same leg of the rotating loop is always connected to the same output terminal. Show that the potential difference between the output terminals is given by E= E0 cos theta (where theta = wt is the angle that the plane of the loop makes with the magnetic field direction at time t), and determine E0 in terms of the loop's length L, width W, the magnetic field strength B, and the loop's angular rotation rate w.

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This solution provides a step-wise response which shows how to calculate the potential difference for this physics-based question. All calculations and equations are included.

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phi=Flux= B A Cos theta = BA Cos wt
where theta = angle that the plane of the loop makes with the magnetic field direction at time t
A=area of the loop=W L

E=Potential ...

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