 # 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 of 1 s, starting at t=0. What is magnitude of the magnetic field at 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, is reversed? Because the inner loop is small, assume is uniform over its area. (e) What emf is induced in the small loop at t=0.5 s?

9 years ago

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 Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums.

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