The graph below shows the magnetic flux through a conducting loop as a function

Question

The graph below shows the magnetic flux through a conducting loop as a function of time. The units of flux are webers, which are equivalent to tesla meters2. The flux in the loop changes because the magnetic field passing through the loop changes. The loop itself is stationary. Assume that the field is uniform and the direction of the field is perpendicular to the plane of the loop.

The loop has a resistance of 0.400 , an area of 2.00 m2, and consists of a single turn. Note that you should be able to do this problem without a calculator.

(a) What is the magnitude of the magnetic field passing through the loop at

t = 15 s?

(b) What is the magnitude of the induced current in the loop at

t = 15 s?

Explanation / Answer

(a) Magnetic flux, = BA

At t = 15 s, = 2 T-m2

=> Magnitude of magnetic field, B = /A = (2 T-m2)/(2 m2) = 1 T

(b) Magnitude of induced emf at t = 15 sec is, = /t = (4 - 0)/(20 - 10) = 0.4 V

=> Magnitude of induced current, I = /R = (0.4 V)/(0.4 ) = 1 A

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