Five loops are formed of copper wire of the same gauge (cross - sectional area).
ID: 1560232 • Letter: F
Question
Five loops are formed of copper wire of the same gauge (cross - sectional area). Loops 1-4 are identical; loop 5 has the same height as the others but is longer. At the instant shown, all the loops are moving at the same speed in the directions indicated. There is a uniform magnetic field pointing out of the page in region I; in region II there is no magnetic field. Ignore any interactions between the loops. a. For any loop that has an induced current, indicate the direction of that current. b. Rank the magnitudes of the emfs around the loops. Explain your reasoning. c. Rank the magnitudes of the currents in the loops. Explain your reasoning.Explanation / Answer
a)
for loop 1:
as the loop goes out of region 1 having magnetic field in outward direction , the outward magnetic flux linked with loop 1 decreases. So to oppose the decrease in the magnetic flux , the loop induces current in itself so as to increase the magnetic flux. it does so by inducing current in such direction that it produce its own magnetic field in the same direction as the external magnetic field (outward). to produce outward magnetic field , the loop induces current in Counter-clockwise direction
for loop 4:
as the loop goes into region 1 having magnetic field in outward direction , the outward magnetic flux linked with loop 4 increases. So to oppose the increase in the magnetic flux , the loop induces current in itself so as to decrease the magnetic flux. it does so by inducing current in such direction that it produce its own magnetic field in the opposite direction as the external magnetic field (outward). to produce inward magnetic field , the loop induces current in clockwise direction
for loop 5:
as the loop goes into region 1 having magnetic field in outward direction , the outward magnetic flux linked with loop 4 increases. So to oppose the increase in the magnetic flux , the loop induces current in itself so as to decrease the magnetic flux. it does so by inducing current in such direction that it produce its own magnetic field in the opposite direction as the external magnetic field (outward). to produce inward magnetic field , the loop induces current in clockwise direction
b)
induced emf is given as
E = B L v
where L = height of loop , v = speed , B = magnetic field in the region
for loop 2 and 3 , there is no change in magnetic flux , hence induced emf in them is 0
1 = 4 = 5 > 2 = 3
c)
the cross-sectional area is same for all the loops wire. length of loop 5 has longer circumference as compared to all other 4 loops , hence R5 has greatest resistance
loop 1 and 4 have same lengths , so same resistance and hence same current since they have equal induced emf in them,
i1 = i4 > i5 > i2 = i3
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