A NONCONDUCTING sphere with uniform volume charge density ? HELP

[SoulofLoneWlf]

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]

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]

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]

… 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]

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]

"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]

"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]

… 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]

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

 

[tiny-tim]

(just got up :zzz:)

makes very little difference

try one and see what you get ​