A conducting loop is made in the form of two squares of sides s 1 = 2.6cm and s

Question

A conducting loop is made in the form of two squares of sides s1 = 2.6cm and s2 = 6.8 cm as shown. At time t = 0, the loop enters a region of length L = 17 cm that contains a uniform magnetic field B = 1.1 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 44 cm/s. The resistance of the loop is R = 2.7 ?.

1)

At time t = t1 = 0.02 s, what is I1, the induced current in the loop? I1 is defined to be positive if it is in the counterclockwise direction.

2)

At time t = t2 = 0.497 s, what is I2, the induced current in the loop? I2 is 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 = 44 cm/s at t = t2 = 0.497 s?

4)

At time t = t3 = 0.406 s, what is I3, the induced current in the loop? I3 is defined to be positive if it is in the counterclockwise direction.

Explanation / Answer

a) at t= 0.02, distance traveled = 0.02*44 = 0.88 cm
so still in s1 area

emf = B L v

I = -B L v/R = -1.1*2.6E-2*.44/2.7= -4.66E-3 A

b) 0.497*44=21.868 cm
so made it way through s1 and part of s2

so I = B L v/R = 1.1*6.8E-2*.44/2.7=1.22E-2 A

3)
F = I L B = 1.22E-2*6.8E-2*1.1= 9.13E-4 N

4) d = 0.406*44=17.86 cm

all the loop is in B and nothing leaving so no change in flux

I = 0

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