A conducting loop is made in the form of two squares of sides s1 = 3.0cm and s2

Question

A conducting loop is made in the form of two squares of sides s1 = 3.0cm and s2 = 6.3 cm as shown. At time t = 0, the loop enters a region of length L = 17.3 cm that contains a uniform magnetic field B = 1.2 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 34.0 cm/s. The resistance of the loop is R = 1.7 ?.

1) At time t = t1= 0.029 s, what is I1, the induced current in the loop? I1is defined to be positive if it is in the counterclockwise direction.

2) At time t = t2= 0.659 s, what is I2, the induced current in the loop? I2is defined to be positive if it is in the counterclockwise direction.

3) What is Fx(t2), the x-component of the force that must be applied to the loop to maintain its constant velocity v = 34.0 cm/s at t = t2= 0.659 s?

Explanation / Answer

1) At time t = t1= 0.029 s, what is I1, the induced current in the loop? I1is defined to be positive if it is in the counterclockwise direction.

i = /R = (1.2*0.03*0.34)/1.7 = -0.0072 A

2) At time t = t2= 0.659 s, what is I2, the induced current in the loop? I2is defined to be positive if it is in the counterclockwise direction.

x = 22.406 - 17.3 = 5.106 cm

i = /R = (1.2*0.063*0.34)/1.7 = +0.0151 A

3) What is Fx(t2), the x-component of the force that must be applied to the loop to maintain its constant velocity v = 34.0 cm/s at t = t2= 0.659 s?

F = i L B = 0.01512 * 0.063 * 1.2 = 0.00114 N

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