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A charge q is circulating with a constan...

A charge q is circulating with a constant speed v in a semicircular loop of wire of radius R. The magnetic moment of this loop is

A

qvR

B

`(piRqv)/(2(pi+2))`

C

`(qvR)/3`

D

`(qvpiR)/(pi+2)`

Text Solution

Verified by Experts

The correct Answer is:
B
When the charge moves along the path ABCA, it travels a distance `= piR + 2R = R(pi + 2)` and the time taken for this is given by
`t="distance"/"velocity" = (R(pi+2))/v`
and the current in the loop `I = q/t=(qv)/(R(pi+2))`
Area of the loop `(A) = (piR^(2))/2`
`therefore` Magnetic moment `M = IA = (qv)/(R(pi+2))xx(piR^(2))/2=(piRqv)/(2(pi+2))`
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