A conducting loop is made in the form of two squares of sides s_1 = 2.7cm and s_

Question

A conducting loop is made in the form of two squares of sides s_1 = 2.7cm and s_2 = 5.6 cm as shown. At time t = 0, the loop enters a region of length L = 16 cm that contains a uniform magnetic field B = 1.8 T, directed in the positive z-direction. the loop continues through the region with constant speed v = 50 cm/s. the resistance of the loop is R = 1 Ohm. At time t = t_1 = 0.018 s, what is I_1, the induced current in the loop? I_1 is defined to be positive if it is in the counterclockwise direction. At time t = t_2 = 0.411 s, what is I_2, the induced current in the loop? I_2 is defined to be positive if it is in the counterclockwise direction. What is F_x(t_2), the x-component of the force that must be applied to the loop to maintain its constant velocity v = 50 cm/s at t = t_2 = 0.411 s? At time t = t_3 = 0.338 s, what is I_3, the induced current in the loop? I_3 is defined to be positive if it is in the counterclockwise direction. Consider the two cases shown above. How does l_I, the magnitude of the induced current in Case I, compare to l_II, the magnitude of the induced current in Case II? Assume s_2 = 3s_1. I_I I_II

Explanation / Answer

1)

emf = B*v*s1 = 1.8*0.5*0.027 = 0.0243 V

current I1 = emf/R = 0.0243/1 = 0.0243 A

2)

emf = B*v*s2 = 1.8*0.5*0.056 = 0.0504 V

current I2 = emf/R = 0.0504/1 = 0.0504 A

3)

F = I2*s2*B = 0.0504*0.056*1.8 = 0.0051 N

4)

distance travelled x = v*t3 = 50*0.338 = 16.9

x > L

emf = B*v*s2 = 1.8*0.5*0.056 = 0.0504 V

current I3 = emf/R = 0.0504/1 = 0.0504 A

5)

III < IIII

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