Acoil is wrapped with 300 turns of wire on the perimeter of a circular frame (radius = 8.0 cm). each turn has the same area, equal to that of the frame. a uniform magnetic field is turned on perpendicular to the plane of the coil. this field changes at a constant rate from 20 to 80 mt in a time of 20 ms. what is the magnitude of the induced emf in the coil at the instant the magnetic field has a magnitude of 50 mt?

Approximately 18 volts when the magnetic field strength increases from to at a constant rate.

Explanation:

By the Faraday's Law of Induction, the EMF that a changing magnetic flux induces in a coil is:

,

where

However, for a coil the magnetic flux is equal to

,

where

For this coil, the magnetic field is perpendicular to coil, so and . The area of this circular coil is equal to .

doesn't change, so the rate of change in the magnetic flux through the coil depends only on the rate of change in the magnetic field strength . The size of the magnetic field at the instant that will not matter as long as the rate of change in is constant.

.

As a result,

.

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