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 = 5.9 cm as shown. At time t = 0, the loop enters a region of length L = 16.7 cm that contains a uniform magnetic field B = 1 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 57 cm/s. The resistance of the loop is R = 1.3 .

1)

At time t = t1 = 0.017 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 = 0.378 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 = 57 cm/s at t = t2 = 0.378 s?

N

4)

At time t = t3 = 0.31 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 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

Explanation / Answer

Ans:-

1] at t = 0.017s l1 = ?

s1 = V*t = 0.57 * 0.017 = 0.00969m

I1 = B*v*s1 /R

     = 1 * 0.57*0.00969 /1.3

     = 4.3*10^-3A         clockwise

2] t = 0.378 s s2 = 0.216m

I2 = 1*0.57*0.216/1.3

   = 0.0947A    counter clockwise

3]F = I*L x B

       =I*L*B*sin 90=ILB

I = B*V*s2 / R = 1*0.57 * 0.216 / 1.3 =0.0947A

F = 0.947* 0.167*1 =0.0158N

4]t3 =0.31s s3 = 0.1767m

I3 =B*V *s3 /R

= 1* 0.57 *0.1767/1.3 = 0.0775A    counter clockwise

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