Derive an expression for the magnetic moment ($\overrightarrow { \mu }$ ) of an electron revolving around the nucleus in terms of its angular momentum ($\overrightarrow { l }$ ). What is the direction of the magnetic moment of the electron with respect to its angular momentum ?
We have u=iA
$=\frac { e.\upsilon }{ 2\pi r } \pi { r }^{ 2 }$
$u=\frac { evr }{ 2 } $
l=mvr
$vr=\frac { l }{ m }$
$\overrightarrow { u } =\frac { -e\overrightarrow { l } }{ 2\quad m } $
The direction of $\overrightarrow { u } $ is opposite to that of $\overrightarrow { l } $ because of the negative charge of the electron.