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What is the magnetic moment of an electr...

What is the magnetic moment of an electron orbiting in a circular orbit of radius r with a speed v?

A

`evr`

B

`(evr)/2`

C

`(ev)/(2r)`

D

`(vr)/(2e)`

Text Solution

Verified by Experts

The correct Answer is:
B
The time taken by an electron to complete one revolution around the nucleus is
`T=("distance")/("velocity")=(2pi r)/v`
`:.` The equivalent current is given by
`I=q/t=e/T=e/((2pi r)/v)=(ev)/(2pi r)`
`:.` Magnetic dipole moment of the electron
= current `xx` Area `=(ev)/(2pi r)xx pi r^(2) =(e vr)/2`
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