Aloop of wire of area 71 cm^2 is placed with its plane parallel to a 16 mt magnetic field. the loop is then rotated so that its plane is perpendicular to the field, in a time of 0.7 s. what is the average emf generated in the coil while the loop is rotating, in units of volts?

Approximately 1.62 × 10⁻⁴ V.

Explanation:

The average EMF in the coil is equal to

,

Why does this formula work?

By Faraday's Law of Induction, the EMF induced in a coil (one loop) is equal to the rate of change in the magnetic flux through the coil.

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Finding the average EMF in the coil is similar to finding the average velocity.

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However, by the Fundamental Theorem of Calculus, integration reverts the action of differentiation. That is:

.

Hence the equation

.

Note that information about the constant term in the original function will be lost. However, since this integral is a definite one, the constant term in won't matter.

Apply this formula to this question. Note that , the magnetic flux through the coil, can be calculated with the equation

.

For this question,

Initial flux: .

Final flux: .

Average EMF, which is the same as the average rate of change in flux:

.