- #1

- 16

- 1

## Homework Statement

Assume that an electron is a sphere of uniform mass density

[itex]\rho_m=\frac{m_e}{\frac{4}{3} \pi r_e^3}[/itex], uniform charge

density [itex]\rho_e=\frac{-e}{\frac{4}{3} \pi r_e^3}[/itex], and

radius [itex]r_e[/itex] rotating at a frequency [itex]\omega[/itex]

about the z-axis. [tex]m_e=9.109*10^{-31}[/tex] kg and

[tex]e=1.602*10^{-19}[/tex] C

Using the formula [tex]\vec{m}=\frac{1}{2} \int \vec{r} \times

\vec{J(\vec{r})} d\tau[/tex], compute the magnetic moment of this

electron. Your answer should depend on e, [tex]\omega[/tex] and

[tex]r_e[/tex]

## Homework Equations

Given above.

## The Attempt at a Solution

Ok, so I know that in general, [tex]\vec {J}=\rho_e \vec {v}[/tex]. I'm not sure how to proceed from here since writing J in terms of omega yields [tex]\vec {J}=\frac {\rho_e \omega}{\vec {r}}[/tex]. I've always heard that dividing by a vector is not strictly defined in a math sense. Either I'm not approaching this in the right way, or putting that funkiness into the cross product above yields some magnificence that I am, as of now, incapable of seeing.

Help will be greatly appreciated.