The square loop in the figure below is made of wires with a total series resista

Question

The square loop in the figure below is made of wires with a total series resistance of 15 Ohm. It is placed in a uniform 0.11 T magnetic field directed perpendicular into the paper. Calculate magnetic flux through the square loop. Now, the direction of the magnetic field is rotated from into the page to 45' to the normal of the paper and its magnitude doubled to 0.22 T. What is the magnitude of the average emf induced in the loop, if these changes occurred over 035 s? If instead the original magnetic field (0.11 T into the paper) is maintained, but the loop is pulled along the arrows to the left and right until the area in the loop is reduced to one third its starting value. What is the magnitude of the average emf induced in the loop, if this process takes 0.24 s? Determine the magnitude and direction of the average current generated in the loop in step (c).

Explanation / Answer

part A :
magnetic flux = phi = BA

phi = 0.11* 3*3

phi = 0.99 Wb

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part B :

induced emf e = N A dB cos 45/dt

emf e = 0.22*1 * 3*3 * cos 45/0.35

emf e = 2.97 Volts

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part C:

area = 3*3/3 = 3 m^2

B = 0.11 T

so emf e = 1 * 3 * 0.11* cos 45/0.35

emf e = 0.495 Volts

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induced current I = emf/R

I = 0.495/15

i = 0.033 Amps

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