Question

A circular loop in the plane of a paper lies in a 0.45 T magnetic field pointing into the paper. The loop's diameter changes from 23.0 cm to 6.8 cmin 0.54 s .

What is the magnitude of the average induced emf?

What is the average induced current if the coil resistance is 3.9 Ω ?

Answer 1

Hi,

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PART 1:

According to Faraday's law, we know that the induced emf in the coil is given by,

Where,

is the change in magnetic flux.

is the magnitude of the magnetic field (T).

is change in area of the coil (m²).

is change in time (s).

For a circular coil, we get, induced emf in the coil is given by,

Where,

is the initial diameter of the coil (m).

is the final diameter of the coil (m).

Given that,

Magnitude of the magnetic field,

Initial diameter of the coil,

Final diameter of the coil,

Change in time,

Induced emf in the coil is given by,

PART 2:

We know that, According to ohm's law, current through the coil is given by,

Where,

is resistance of the coil (ohms).

Given that,

Resistance of the coil,

Current through the coil is given by,

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