A circular coil enclosing an area of 97 cm2 is made of 200 turns of copper wire.

Question

A circular coil enclosing an area of 97 cm2 is made of 200 turns of copper wire. The wire making up the coil has resistance of 5.0 , and the ends of the wire are connected to form a closed circuit. Initially, a 2.0 T uniform magnetic field points perpendicularly upward through the plane of the coil. The direction of the field then reverses so that the final magnetic field has a magnitude of 2.0 T and points downward through the coil. If the time required for the field to reverse directions is 0.12 s, what average current flows through the coil during that time?

Explanation / Answer

The quantity symbolised by B and measured in teslas (T) is magnetic flux density. Magnetic field (H) is a completely different concept, and its units are amps/metre. If you intend to get anywhere in the topic of magnetism you must get used to using the correct terminology, symbols, units, etc, and distinguish between different concepts clearly. I shall treat the question as though all references to ‘magnetic field’ are in fact intended to be to ‘flux density’.

To answer the question you use Faraday's law of electromagnetic induction: V = dF/dt where dF/dt is the rate of change of flux linkages in a circuit in which a voltage V is induced. Flux linkage is flux*(turns (n)). In the case of a uniform flux density B passing though a plane loop of area A, the normal to the plane being parallel to the direction of B, flux = A*B, and F = n*A*B.

In your problem, the average rate of change of flux linkage is n*2*A*B/t where t is the time taken for B to fall to zero and then reverse.

so we can write V = n*B*2*pi*r^2/t, and I = V/R = n*B*pi*r^2/t*5

( the resistance (R) is 5 ohms).

This evaluates to 16.16666 A

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