A conducting loop is made in the form of two squares of sides s 1 = 2.9cm and s

Question

A conducting loop is made in the form of two squares of sides s1 = 2.9cm and s2 = 7.5 cm as shown. At time t = 0, the loop enters a region of length L = 18.3 cm that contains a uniform magnetic field B = 1.6 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 30 cm/s. The resistance of the loop is R = 1.4 ?.

1)At time t = t1= 0.032 s, what is I1, the induced current in the loop? I1is defined to be positive if it is in the counterclockwise direction.

A

2)At time t = t2= 0.79 s, what is I2, the induced current in the loop? I2is defined to be positive if it is in the counterclockwise direction.

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 = 30 cm/s at t = t2= 0.79 s?

N

4)At time t = t3= 0.642 s, what is I3, the induced current in the loop? I3is defined to be positive if it is in the counterclockwise direction.

A

5)Consider the two cases shown above. How does II, the magnitude of the induced current in Case I, compare to III, the magnitude of the induced current in Case II? Assume s2= 3s1.

II < III

II = III

II > III

A conducting loop is made in the form of two squares of sides s1 = 2.9cm and s2 = 7.5 cm as shown. At time t = 0, the loop enters a region of length L = 18.3 cm that contains a uniform magnetic field B = 1.6 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 30 cm/s. The resistance of the loop is R = 1.4 ?. 1)At time t = t1 = 0.032 s, what is I1, the induced current in the loop? I1 is defined to be positive if it is in the counterclockwise direction. A 2)At time t = t2 = 0.79 s, what is I2, the induced current in the loop? I2 is defined to be positive if it is in the counterclockwise direction. 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 = 30 cm/s at t = t2 = 0.79 s? N 4)At time t = t3 = 0.642 s, what is I3, the induced current in the loop? I3 is defined to be positive if it is in the counterclockwise direction. A 5)Consider the two cases shown above. How does I1, the magnitude of the induced current in Case I, compare to III, the magnitude of the induced current in Case II? Assume s2 = 3s1.

Explanation / Answer

a)

Here emf is induced by the right side s1 moving into the field

E=B*V*S1=1.6*0.3*0.029

E=0.01392 volts

Induced current in the loop is

I=E/R =0.01392/1.4

I=9.94*10-3 A

Induced current creates a magnetic field that opposes th change in flux .Flux is increasing out of page ,so current is in clockwise direction

I=-0.00994 A or -9.94*10-3 A

b)

Induced emf

E=B*V*S2=1.6*0.3*0.075

E=0.036 Volts

Induced current in the loop

I=0.036/1.4=0.0257 A

Here change in flux is decreasing ,so current is counter clockwise direction.so

I=0.0257 A

c)

Physical power applied must be equal to electricla power dissipated ,so

P=F*v=E2/R

F=(1/v)*(E2/R)

so

Fx(t2)=(1/0.3)(0.0362/1.4)

Fx(t2)=3.086*10-3 N or 0.003086 N

d)

Here flux is decreasing ,so current is in counterclockwise direction ,so

I=0.00994 A or -9.94*10-3 A

e)

|| < ||| is the answer

since In case 1 ,

Induced Current

I1=EBS1/R

In case 2

Induced current

I=EB(S2-S1)/R

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