A circular loop of wire with a radius of 15.0 cm and oriented in the horizontal xy-plane is located in a region of uniform magnetic field. A field of 1.5 T is directed along the positive z-direction, which is upward. Of the loop is removed from the field region in a time interval of 2.8 ms , find the average emf that will be induced in the wire loop during the extraction process.

The average emf that will be induced in the wire loop during the extraction process is 37.9 V

Explanation:

The average emf induced can be calculated from the formula

Where is the number of turns

is the change in magnetic  flux

is the time interval

The change in magnetic flux is given by

Where is the final magnetic flux

and is the initial magnetic flux

Magnetic flux is given by the formula

Where is the magnetic field

is the area

and is the angle between the magnetic field and the area.

Initially, the magnetic field and the area are pointed in the same direction, that is,

From the question,

B = 1.5 T

and radius = 15.0 cm = 0.15 m

Since it is a circular loop of wire, the area is given by

∴

∴

( NOTE: )

Wb

For

The field pointed upwards, that is . Since

Then

Hence,

From the question

Here, = 1

Hence,

becomes

Hence, the average emf that will be induced in the wire loop during the extraction process is 37.9 V.

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