Shrinking Loop. A circular loop of flexible iron wire has an initial circumferen

Question

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 162 cm , but its circumference is decreasing at a constant rate of 15.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.500 T , which is oriented perpendicular to the plane of the loop. Assume that you are facing the loop and that the magnetic field points into the loop.

Part A

Find the magnitude of the emf E induced in the loop after exactly time 8.00 s has passed since the circumference of the loop started to decrease.

Express your answer numerically in volts to three significant figures.

Part B

Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.

Explanation / Answer

a)

Given that initial circuference is 2*pi*r1 = 162 cm

radius of the loop is r1 = 162/(2*3.142) = 25.78 cm

Area of cross section is A1 = pi*r1^2 = 3.142*0.2577^2 = 0.208 m^2

initial flux through loop is phi_1 = B*A = 0.5*0.208 = 0.104

Finally after 8 sec,the circumference is 2*pi*r2 = 162-(8*15) = 42 cm

radius of the loop is r2 = 0.42/(2*3.142)= 0.0668

Final area of cross section is A2 = pi*r2^2 = 3.142*0.0668^2 = 0.014 m^2

Final flux through the loop is phi_2 = B*A = 0.5*0.014 = 0.007 Wb

chnage in flux is phi_2-phi_1 = 0.007-0.104 = -0.097 Wb

rate of change of magnetic flux is d(phi_B)/dt = 0.097/8 = 0.012125 Wb/sec

emf E = d(phi_B)/dt = 0.012125 V

B) According to Lenz's law the direction of current is counter clockwise direction

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