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The two terminals of a 20 resistor are connected to one another by a single wire

ID: 1979660 • Letter: T

Question

The two terminals of a 20 resistor are connected to one another by a single wire of length 18 cm. The wire is fashioned into the shape of a circle and is oriented so that it lies in a horizontal plane. The resistor is so tiny that the circumference of the wire loop is, to a very good approximation, just 18 cm. Moreover the resistance of the wire is negligible compared to that of the 20 resistor, so that the resistance of the loop is, to a very good approximation, just 20 . As it happens, this loop is immersed in a uniform, vertical (upward) magnetic field of strength 0.26 T. Over a time span of 2.0 s, the magnetic field is rotated by 180 degrees about a horizontal axis so that it finally points downward. As a consequence, the magnetic field no longer points upward through the loop, but instead points downward. Determine the total amount of charge that flowed through the resistor.

Explanation / Answer

L=18cm=0.18m
A=L2/(4)=2.58*10-3m2

B=0.26T

1=BAcos0o=6.7*10-4Wb

2=BAcos180o=-6.7*10-4Wb

R=20

q=(1-2)/R=6.7*10-5C