A conducting loop is made in the form of two squares of sides s 1 = 3.6cm and s

Question

A conducting loop is made in the form of two squares of sides s1 = 3.6cm and s2 = 7.5 cm as shown.  At time t = 0, the loop enters a region of length L = 19.7 cm that contains a uniform magnetic field B = 1.9 T, directed in the positive z-direction.  The loop continues through the region with constant speed v = 58 cm/s.  The resistance of the loop is R = 2.7 ?.

1) At time t = t1 = 0.021 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 = 0.445 s, what is I2, the induced current in the loop?    I2 is defined to be  positive if it is in the counterclockwise direction.         

4) At time t = t3 = 0.36 s, what is I3, the induced current in the loop?    I3 is defined to be  positive if it is in the counterclockwise direction.         

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.             

A conducting loop is made in the form of two squares of sides s1 = 3.6cm and s2 = 7.5 cm as shown. At time t = 0, the loop enters a region of length L = 19.7 cm that contains a uniform magnetic field B = 1.9 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 58 cm/s. The resistance of the loop is R = 2.7 ?.At time t = t1 = 0.021 s, what is I1, the induced current in the loop? I1 is defined to be positive if it is in the counterclockwise direction. At time t = t2 = 0.445 s, what is I2, the induced current in the loop? I2 is defined to be positive if it is in the counterclockwise direction. What is Fx(t2), the x-component of the force that must be applied to the loop to maintain its constant velocity v = 58 cm/s at t = t2 = 0.445 s? At time t = t3 = 0.36 s, what is I3, the induced current in the loop? I3 is defined to be positive if it is in the counterclockwise direction. 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.

Explanation / Answer

time take to cross length L = 19.7cm,

t = 19.7/58

= 0.34 sec

time taken to cross length L by s1 = (19.7+3.7/58)

= 0.40 sec

so s1 will be crossing the boundary

induced current = B.s1.v/R

= 0.01469 Amp

5. case |

I1 = 0.01469

case ||

I2 = 0.01469+ Is2

so I1 < I2

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