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

AI Thread Summary
Electric potential varies inside and on the surface of a charged sphere due to the distribution of charge, which accumulates only on the surface. The electric field inside the sphere is zero, indicating a constant potential, but this does not mean the potential itself is zero. The capacitance of a charged sphere is inversely related to its radius, leading to a higher potential for smaller spheres when compared to larger ones. Consequently, the potential at the center of the smaller sphere (V1) is greater than the potential at the surface of the larger sphere (V4, V5, V6), which are all equal. This explains the observed variation in electric potential across different regions of the charged sphere.
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Homework Statement


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Homework Equations


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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?...
 
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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
 

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