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Find the surface charge density of a perfect conductor

  • Thread starter MrBoomer
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This is for extra credit not actual homework but I need the points and I would like to understand the subject matter as well so any help would be much obliged.

Homework Statement


There is a sphere with radius R made up of a perfect conducting material in a constant and uniform electric field E. I am tasked to find the surface charge density ρ.


Homework Equations


See #3 for the relevant equations that I used.


The Attempt at a Solution


I am attempting to solve this problem by Gauss's Law. I am almost done, all I need to do is actually construct the sphere...I think.

Since the electric field, E, is 0 in in the sphere the surface charge density is going to be the charge due to the sphere being in the field E.

I assumed [itex]\Phi[/itex] = ERcos[itex]\Theta[/itex] and then assumed that [itex]_{Q}A[/itex] would be the surface charge density (the enclosed charge in the sphere) = [itex]\Phi[/itex]*[itex]_{\epsilon}0[/itex]

However this doesn't help because I didn't construct any sphere and that is where I am lost. That is assuming I am doing this correctly. If I am not please tell me.
 

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