The figure above shows a circular loop with area 0.87m2 and resistance 7.5? that

Question

The figure above shows a circular loop with area 0.87m2 and resistance 7.5? that lies in a plane of the
page. A magnetic field B directed into the page exists in the area of the loop. The field varies with time t,
as shown below. A generic form of any equations used would be much appreciated!

1. Write an equation describing the magnitude of the induced emf in the loop for the interval t = 0 s to t = 8 s.
2. Calculate the magnitude of the current I in the loop at t = 4 s.
3. Sketch a graph of the induced current I as a function of time t for the interval t = 0 s to t = 8 s. Let
above the time axis represent counter clockwise current and below the time axis represent clockwise
movement.
4. Explain your reasoning for each segment of the graph you produced in the previous part.
5. Calculate the total energy dissipated in the loop during the 8.0 s interval.

Explanation / Answer

We know that,

Induced Emf = N d? / dt

where ? = BA, For this loop, N = 1

so, Emf = NA dB/dt

Emf = 1*A * (-0.05*1.8 e-0.05t)

Emf = - 0 .09Ae-0.05t

Magntidue of Emf = 0.09*0.87*e-0.05t

Magnitude of Emf = 0.0783e-0.05t

b) At t = 4 ,

Emf = 0.0783 e-0.05(4)

Emf = 0.0641

so, I = 0.0641 / 7.5

I = 0.008547 amps

Graph of induced current will be same as graph of induced emf where current will change as per dB/dt

Power dissipated can be calculated as

P = I2R

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