Problem 4. XXX X X X X X X XXXXXXXXX XX X X X X X X X XXXXXXXXX XXXXXXXXX XXXXXX

Question

Problem 4. XXX X X X X X X XXXXXXXXX XX X X X X X X X XXXXXXXXX XXXXXXXXX XXXXXXXXX A rectangular coil containing 20 loops (turns) is moving with a constant speed of 5.00 cm/s toward a region containing a uniform magnetic field of 3.00T pointing into the page. The dimensions of the coil are a = 8.00 cm and b = 12.0 cm. The coil has a total resistance of 8.00 N. (a) Consider four different situations: the coil is completely outside the field, half the coil has entered the field, the coil is entirely within the field, 75% of the coil has exited the field. In each of the four situations, determine the induced emf and induced current in the coil. If the current is non-zero, use Lenz's law to determine if it is clockwise or counterclockwise. (b) Compare the situation when half the coil has entered the field to the one when only 25% of it has entered the field. Explain why the induced emf is the same in both cases.

Explanation / Answer

a)

N = 20

B = 3 T

R = 8 Ohms

v = 0.05 m/s

Now , when the loop is completely out of field

as there is no change in magnetic flux in the loop ,

the induced current is zero

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when the loop is half inside the field

Induced current = N * v * B L/R

Induced current = 20 * 3 * 0.05 * 0.08/8

Induced current = 0.03 A

the current is Counterclockwise
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when the loop is entirely inside the field

as there is no change in magnetic flux in the loop ,

the induced current is zero

--

when the loop is 75 % inside the field

Induced current = N * v * B L/R

Induced current = 20 * 3 * 0.05 * 0.08/8

Induced current = 0.03 A

the current is Counterclockwise

b) as the induced current is dependent on rate of change of magnetic flux

and the rate of change of flux is same in both

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