# A NONCONDUCTING sphere with uniform volume charge density ? HELP

#### SoulofLoneWlf

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

1. 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 ?

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#### 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! #### SoulofLoneWlf

Re: A NONCONDUCTING sphere with uniform volume charge density ? 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? #### SoulofLoneWlf

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

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?)

#### SoulofLoneWlf

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

"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

#### SoulofLoneWlf

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

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

#### tiny-tim

try one and see what you get 