- #1
PsychoDash
- 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.