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Question

A circular coil of radius 8.0 cm and 20 turns is rotated about itsvertical diameter with an angular speed of 50 rad s–1 in a uniformhorizontal magnetic field of magnitude 3.0 × 10–2 T. Obtain themaximum and average emf induced in the coil. If the coil forms aclosed loop of resistance 10 W, calculate the maximum value of currentin the coil. Calculate the average power loss due to Joule heating.Where does this power come from?

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Solution

Given: The radius of the circular coil is

The area of the coil is given as,

Where, the radius of the circular coil is

By substituting the given values in the above formula, we get

The maximum induced emf is given as,

Where, the magnetic field strength is

By substituting the given values in the above formula, we get

Thus, the maximum induced emf is

The average emf induced in the coil over a full cycle will be zero.

The maximum current in the coil is given as,

Where, the resistance is

By substituting the given values in the above formula, we get

Thus, the maximum current in the coil is

The average power loss due to joule heating is given as,

Where, the average power loss is

By substituting the given values in the above formula, we get

Thus, the average power loss is

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