A NONCONDUCTING sphere with uniform volume charge density ? HELP

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SUMMARY

The discussion centers on calculating the magnetic field at the center of a nonconducting sphere with uniform volume charge density, total charge Q, and radius α, which rotates about its center with a constant angular velocity ω. Participants clarify that a nonconducting sphere can maintain charge density because the charges remain fixed within it. The magnetic field generated by the moving charges is derived using the formula B = (μ₀/4π) * (qv x ȓ) / r², and suggestions are made to simplify the integration by considering cylindrical shells or circles.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically magnetic fields generated by moving charges.
  • Familiarity with Gaussian surfaces and their application in electrostatics.
  • Knowledge of the magnetic moment and its calculation.
  • Basic calculus skills for integration in three dimensions.
NEXT STEPS
  • Study the derivation of the magnetic field from a rotating charged sphere using the Biot-Savart Law.
  • Learn about the concept of magnetic moment and its significance in electromagnetism.
  • Explore the use of cylindrical coordinates in simplifying integrals involving spherical charge distributions.
  • Investigate the differences between conducting and nonconducting materials in terms of charge distribution and magnetic field generation.
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This discussion is beneficial for physics students, particularly those studying electromagnetism, as well as educators seeking to clarify concepts related to magnetic fields and charge distributions in nonconducting materials.

SoulofLoneWlf
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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 ?
 
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Hi SoulofLoneWlf! :smile:
SoulofLoneWlf said:
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 \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! :smile:
 


Hello tiny time :)
and thanks for clarifying the non conducting part ;)
tiny-tim said:
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 ?
 
SoulofLoneWlf said:
… 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? :wink:​
 


tiny-tim said:
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)*\alpha
 
"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?)
 


tiny-tim said:
"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 \hat{r})/r^2 ??
and to simplify integration of a sphere consider it a circle? 0 to pie?
 
SoulofLoneWlf said:
… magnetic field of a moving charge would then be

B=(μ_o/4∏)*(qv x \hat{r})/r^2 ??

yes :smile:

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 :)
 
  • #10
(just got up :zzz:)

makes very little difference

try one and see what you get :smile:​
 

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