Question

The magnetic moment of an electron orbiting in a circular orbit of radius r with a speed v is equal to:

• A. evr/2
• B. evr
• C. er/2v
• D. None of these

Answer 1

Answer: (A)

evr/2

Answer 2

Magnetic moment μ = niA

Where n = number of turns of the current loop

I = current; Since the orbiting electron behaves as a current loop of current i, we can write

$\mathrm { i } = \frac { \mathrm { e } } { \mathrm { T } } = \frac { \mathrm { e } } { \frac { 2 \pi \mathrm { r } } { \mathrm { v } } } = \frac { \mathrm { ev } } { 2 \pi \mathrm { r } }$

A = area of the loop = πr²

$\Rightarrow \mu = ( 1 ) \left( \frac { \mathrm { ev } } { 2 \pi \mathrm { r } } \right) \left( \pi \mathrm { r } ^ { 2 } \right)$ = $\frac { \mathrm { evr } } { 2 }$ .

Hence (1) is correct