An electron of charge e moves in a circular orbit of radius r around the nucleus at a frequency v. The magnetic moment associated with the orbital motion of the electron is

Question

An electron of charge e moves in a circular orbit of radius r around the nucleus at a frequency v. The magnetic moment associated with the orbital motion of the electron is (A)  π ver2  (B)  (π vr2/e)  (C)  (π v e/r)  (D)  (π vr2/v)

Tardigrade Admin · Accepted Answer

Magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. It is given by

μ = I A

.. (i) where

I

is current and

A

the area. The effective current

(I)

is

I = \frac{e}{T}

where

e

is electron charge and

T

the time period. Also,

v = \frac{1}{T} =

frequency and area

A = π r^{2}

, where

r

is radius of circular path. Putting these values in Eq. (i), we get

μ = e v . π r^{2}

Note: Magnetic moment can also expressed terms of angular momentum

(L)

μ = I A = - \frac{2}{2 M _{e}} L

. where

M_{e}

is mass of electron.

Q. An electron of charge e moves in a circular orbit of radius r around the nucleus at a frequency v. The magnetic moment associated with the orbital motion of the electron is

$π v e r^{2}$

$\frac{π v r ^{2}}{e}$

$\frac{π v e}{r}$

$\frac{π v r ^{2}}{v}$

Q. An electron of charge e moves in a circular orbit of radius r around the nucleus at a frequency v. The magnetic moment associated with the orbital motion of the electron is

πver2

eπvr2​

rπve​

vπvr2​

$π v e r^{2}$

$\frac{π v r ^{2}}{e}$

$\frac{π v e}{r}$

$\frac{π v r ^{2}}{v}$