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. 1) 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. 2) 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. 3) 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? 4) 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.

Explanation / Answer

at t1 = 0.018 s

d1 = v x t1 = 0.5 m/s x 0.018 = 0.009 m

the d1 is less than s1, so

e = B v s1

e = 1.8 x 0.5 x 0.027 = 0.0243 Volts

I1 = e/R = 0.0243/1 = 0.0243 A

Hence, I1 =-0.0243 A (should be negative, because flux is increasing)

4)d3 = v t3

d3 = 0.5 x 0.338 = 0.169 m

Again its less than s1

e = B v L = 1.8 x 0.5 x 0.027 = 0.0243

I3 = 0.0243/1 = 0.0243 A (positive since flux is decreasing)

I3 = + 0.0243 A

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