# A NONCONDUCTING sphere with uniform volume charge density ? HELP

A NONCONDUCTING sphere with uniform volume charge density ? HELP!!

## Homework Statement

so this is the problem,
a nonconducting sphere of radius $\alpha$ has a uniform volume charge density with total charge Q. the sphere rotates about an axis through its center with constant angular velocity $\varpi$ . Find the magnetic field at the center of the sphere.

ALSO, how is a non conducting sphere able to have charge density ?

tiny-tim
Homework Helper
Hi SoulofLoneWlf!
ALSO, how is a non conducting sphere able to have charge density ?

Why not? It's con-conducting, so if we place charges anywhere inside it, they stay there!
a nonconducting sphere of radius $\alpha$ has a uniform volume charge density with total charge Q. the sphere rotates about an axis through its center with constant angular velocity $\varpi$ . Find the magnetic field at the center of the sphere.

Show us what you've tried, and where you're stuck, and then we'll know how to help!

Hello tiny time :)
and thanks for clarifying the non conducting part ;)
Hi SoulofLoneWlf!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

Well to be honest i don't know where to start i know i can find the e field by placing it inside a gaussian surface (bigger sphere) but that is really all i have which isn't really the scope of this problem i think ?

tiny-tim
Homework Helper
… the sphere rotates about an axis through its center with constant angular velocity $\varpi$ . Find the magnetic field at the center of the sphere.

a stationary charge has no magnetic field

a moving charge has a magnetic field

what method can you use to sum the magnetic fields of all the charges?

a stationary charge has no magnetic field

a moving charge has a magnetic field

what method can you use to sum the magnetic fields of all the charges?

so then the magnetic moment of each charge would be usable?
μ=Q/(2Mass)*$\alpha$

tiny-tim
Homework Helper
"magnetic moment"?

what is the magnetic field of a moving charge?​

(and how can you split the sphere up so as to simplify the integration?)

"magnetic moment"?

what is the magnetic field of a moving charge?​

(and how can you split the sphere up so as to simplify the integration?)

sorry i guess i took a wrong turn on this one but magnetic field of a moving charge would then be

B=(μ_o/4∏)*(qv x $\hat{r}$)/r^2 ??
and to simplify integration of a sphere consider it a circle? 0 to pie?

tiny-tim
Homework Helper
… magnetic field of a moving charge would then be

B=(μ_o/4∏)*(qv x $\hat{r}$)/r^2 ??

yes

you can use cylindrical shells, or circles

which approach would you recommend ? to use on this one? circles?
by the way thank you for your help so far :)

tiny-tim