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A NONCONDUCTING sphere with uniform volume charge density ? HELP

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

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

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

tiny-tim

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Hi SoulofLoneWlf! :smile:
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! :biggrin:
a nonconducting sphere of radius [itex]\alpha[/itex] has a uniform volume charge density with total charge Q. the sphere rotates about an axis through its center with constant angular velocity [itex]\varpi[/itex] . 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! :smile:
 
Re: A NONCONDUCTING sphere with uniform volume charge density ? HELP!!

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

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

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… the sphere rotates about an axis through its center with constant angular velocity [itex]\varpi[/itex] . 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? :wink:
 
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? :wink:
so then the magnetic moment of each charge would be usable?
μ=Q/(2Mass)*[itex]\alpha[/itex]
 

tiny-tim

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"magnetic moment"? :confused:

what is the magnetic field of a moving charge?​

(and how can you split the sphere up so as to simplify the integration?)
 
Re: A NONCONDUCTING sphere with uniform volume charge density ? HELP!!

"magnetic moment"? :confused:

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 [itex]\hat{r}[/itex])/r^2 ??
and to simplify integration of a sphere consider it a circle? 0 to pie?
 

tiny-tim

Science Advisor
Homework Helper
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… magnetic field of a moving charge would then be

B=(μ_o/4∏)*(qv x [itex]\hat{r}[/itex])/r^2 ??
yes :smile:

you can use cylindrical shells, or circles
 
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

Science Advisor
Homework Helper
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(just got up :zzz:)

makes very little difference

try one and see what you get :smile:
 

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