Why Does Electric Potential Vary Inside and On the Surface of a Charged Sphere?

[erinec]

Homework Statement

http://img156.imageshack.us/img156/2111/picture2ox5.png

Homework Equations

N/A

The Attempt at a Solution

The correct answer is supposed to be: V1 > V2 > V3 > V4 = V5 = V6

But it is kind of weird...

since charge only accumulates at the surface, you would think that V1=V4=V5=V6=0.

My question is: Why is V1 randomly higher?...

 

[snapback]

hi erinec,

it is the resultant electric field which is zero in a sphere (due to charge accumulation on the surface) but a zero fiel means a constant potential (and not zero potential) , that's why V4=V5=V6

the capacitance of a charged sphere is C=4*pi*eps0*R, this means smaller C for the smaller sphere. Now it is Q=C*V -> V=Q/C -> the surface of the smaller sphere has a higher potential V (for a charge coming from infinity) than the surface of the larger sphere. Inside of the smaller sphere, the potential is again constant. This gives V1>V4=V5=V6