Homework Help: Electric potential of a solid copper sphere

bfusco · Sep 23, 2012

1. The problem statement, all variables and given/known data
An isolated solid copper sphere of radius .12m has a positive charge of 6.4x10^-9 C.
i) calculate the electric potential at a point .10 m from the center of the sphere.
ii)calculate the electric potential at a point .24 m from the center of the sphere.

3. The attempt at a solution
i) originally i thought the answer was 0 because since the sphere is copper it is conducting, so all the charge is on the surface of the sphere so at a distance .1 m (not reaching the surface) i assumed the potential was 0. i now know that this is incorrect. if someone could explain that to me i would appreciate it. is it because the electric potential doesn't work exactly like Gauss' law in that where the charge is matters.

ii)i used the equation V=kQ/R, however instead of using the .24 meters from the center, i used .12 m as R because the charge is at the surface, so a point .12m away from the surface of the sphere is only .12 m away from the charge. its apparently wrong and i dont understand why.

BruceW · Sep 23, 2012

bfusco said: ↑

i) originally i thought the answer was 0 because since the sphere is copper it is conducting, so all the charge is on the surface of the sphere so at a distance .1 m (not reaching the surface) i assumed the potential was 0. i now know that this is incorrect. if someone could explain that to me i would appreciate it. is it because the electric potential doesn't work exactly like Gauss' law in that where the charge is matters.

You're right that all the charge would be on the surface of the sphere. But this does not mean the potential is zero inside the sphere. You should really try to do the second problem, so you can work out the potential at the surface of the sphere, then you can work out what it should be inside the sphere.

bfusco said:

ii)i used the equation V=kQ/R, however instead of using the .24 meters from the center, i used .12 m as R because the charge is at the surface, so a point .12m away from the surface of the sphere is only .12 m away from the charge. its apparently wrong and i dont understand why.

You've used the equation V=kQ/R, and used the distance R to mean the distance from the nearest point on the sphere to wherever you are calculating V to be. But of course, the charge is going to be spread all over the surface of the sphere, so you should really be doing an integral over all the charges, where R is a variable. But luckily, the answer is quite simple for a charge distribution which is spread over the surface of a sphere, so you shouldn't have to do an annoying integral. Think about the symmetry of the problem. You've mentioned Gauss' law, so try to use that to show the answer.

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Homework Help: Electric potential of a solid copper sphere

bfusco

BruceW