1.

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

Answer»

QVR
`(piRqv)/(2(pi+2))`
`(qvR)/3`
`(qvpiR)/(pi+2)`

Solution :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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