How Is the Potential Inside a Charged Sphere Constant?

[svar]

can someone explain how the potential inside a sphere is constant, in terms of using coulomb's law and knowledge of charge in an electric field, without directly invoking gauss's law or the partial derivative for rate of change in potential.

the graphs depicting potential around a sphere show (symmetrical) inverse-distance relationship rising to a maximum value of potental at the surface of the sphere, then the line flattens to show constant value right across one side of sphere to the other passing through the centre of sphere. my question is how to explain the value of potential is constant inside the sphere.

 

[olgranpappy]

can someone explain how the potential inside a sphere is constant,

it's not. the potential inside any arbitrary sphere is not constant. can you further specify the properties of this sphere for that we know what you are trying to say?

in terms of using coulomb's law and knowledge of charge in an electric field, without directly invoking gauss's law or the partial derivative for rate of change in potential.

the graphs depicting potential around a sphere show (symmetrical) inverse-distance relationship rising to a maximum value of potental at the surface of the sphere, then the line flattens to show constant value right across one side of sphere to the other passing through the centre of sphere. my question is how to explain the value of potential is constant inside the sphere.

 

[svar]

thanks folks, problem solved, thanks to prof. walter lewin of MIT on his utube lectures.

If E inside the sphere is zero, then F on a charge in the sphere is zero, therefore W done on the charge is zero as it moves about in the sphere, delta V is therefore zero, and V = the the value at the surface.