The square loop shown is made of wires with a total series resistance of 20 Ohm.

Question

The square loop shown is made of wires with a total series resistance of 20 Ohm. It is placed in a uniform 1 T magnetic field directed perpendicular into the plane of the paper. The loop, which is hinged in each comer, is pulled as shown until the separation between points A and B is 3.0 m (so the diamond shape "squishes" down but the sides stay the same length). Note that the angle 0 drops from 45 astir to zero. If this process takes 0.5 s, what is the magnitude and direction of the average current generated in the loop?

Explanation / Answer

Let O be the center of the rhombus circuit loop. We have OP = OQ = 1.5m. The distance from O to any pulled point is: (3^2-1.5^2) = 2.598(M). Hence the circuit loop's final area is:
2*1.5*2.598 = 7.794 (m^2)

The original area of the circuit loop is: 1.5*1.5 = 2.25 (m^2)
According to Faraday's Law of Induction, we have the MAGNITUDE of the average current generated in the loop:
I = E/R = (-d/dt)/(4*20) = 1*(7.794-2.25)/(0.5*4*20) = 0.1386 (A)
The current is clockwise.

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