# Equipotential with Spherical Conductors

1. Oct 16, 2011

### calvinjhfeng

For electrostatics, I know that conductors have 0 electric field inside. And I know that the surface of a spherical conductor has equipotential, (Maybe this is true for all shape of conductor in equilibrium right? ).

So my question is, is the potential 0 inside a conductor as well?

Is it only equipotential from surface to very far away from the spherical conductor?
The inside and outside of the conductor are not equipotential "equal in potential" ?

Thanks so much for your time.

2. Oct 17, 2011

### chrisbaird

The electric field is defined as the negative gradient of the electric potential. Because the derivative of a constant is zero, you can always add a constant to the electric potential and still get the same physics, only potential differences matter. To avoid confusion, we typically pick some reference point (the ground) and call the potential at that point zero, and then calculate all other potentials in the system relative to that point. So a grounded conductor has a potential of zero everywhere on its surface and everywhere in its interior. But an ungrounded conductor (higher potential relative to some ground) will have some nonzero potential V everywhere on its surface and everywhere interior. All points on the surface and inside a perfect conductor are equal in potential and define a region we call the equipotential.

The equipotential is only right on the surface of the conductor. As soon as you move away in space from the surface, the potential will change.