A small circular loop of area 2 cm2 is placed in the plane of, and concentric with, a large circular loop of radius 1 m. The current in the large loop is changed at constant rate from 200A to -200A ( a change in direction) in a time of1 s, starting at t=0. What is magnitude of the magnetic fieldat the center of the small loop due to the current in the large loop at (a) t=0, (b) t=0.5 s, and (c) t=1 s? (d) from t=0 to t=1 s, isreversed? Because the inner loop is small, assumeis uniform over its area. (e) What emf is induced in the small loop at t=0.5 s?

Dear Sandeep,

a)
The equation for the current as a function of time is given by
I = I₀ (1 - 2t)
The magnetic field at the center of a current loop is given by

At t = 0, the current is 200 A, so the magnetic field is given by


At t = .5, the current is 0 A, so the magnetic field is zero. At t = 1, the current is -200 A, so the magnetic field is given by

b)
The magnetic flux through the loop is given by

Here, we take .
So, the flux is given by

The area of the loop is given by

So, the change in magnetic flux over time is given by

Since A, R, and are constants in time, this becomes


Well, the change in magnetic flux over time is known as the EMF, so we write it as such.

Plugging in the numbers, we find that

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