An electron moves with a constant speed v along a circle of radius r.(a) find the equivalent current through a point on its path.(b) Find the magnetic moment of the circulating electron.(c ) Find the ratio of the magnetic moment to the angular momentum of the electron.

Explanation

(a) `T = (2pi r)/(v)`
`i = (q)/(T) = (e)/(2pi r//v) = (ev)/(2pi r)`, current is anticlockwise

(b) `M = iA = (ev)/(2pi r)pi r^(2) = (ev r)/(2), o.`
( c) Angular momentum of electron
`L = mvr, ox`
`(M)/(L) = (evr//2)/(mvr) =(e)/(2m)`
`(vec(M))/(vec(L)) = -(e)/(2m)` (the direction of two vectors are just opposite)