Four conducting loops, all of the same resistance, are moving with the velocitie

Question

Four conducting loops, all of the same resistance, are moving with the velocities indicated either into (loops 1 and 4) or out of (loops 2 and 3) a region of magnetic field. The field has the same magnitude within the rectangular region, but is directed into the page in the left half of the region and out of the page in the right half. (a) Rank the four loops based on the magnitude of their induced current, from largest to smallest, at the instant shown in the picture. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.) (b) Now, let's define counterclockwise to be the positive direction for current. Rank the four loops based on the induced current, from most positive to most negative, at the instant shown in the picture. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)

Explanation / Answer

a) Use equation F= BLv

Since for loop 2 and loop 4 Bnet = 0 T , emf for these loop = 0 V

Thus e2 and e4 = 0 V

Since for loop 3 velocity is double the velocity of loop1 but half length of the side

e3 =e1

Thus we can rank emfs e1, e2, e3 and e4 as below,

e1=e3<e2=e4

b) To get direction of I use figure below,

e1 >e2=e4>e3

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