Electric Field and Potential in a Conductor: Zero at the Surface?

[aftershock]

I understand that if two points are inside a conductor they're at the same potential. I also understand that if two points lie on the surface of the conductor they're at the same potential.

If point a lies on the surface of a conductor and point b lies inside is there still zero potential difference between a and b?

If so, does that mean the electric field at the surface of a conductor is also zero?

 

[Born2bwire]

For you first point, yes. The entire volume of a conductor is equipotential. However, that does not mean that the electric field at the surface is zero. The tangential electric field is zero, but the normal electric field is non-zero. The non-zero normal field is a result of the charge that builds up on the surface of the conductor in response to the applied electric field.

 

[andrien]

electric field inside the conductor is zero in static situation.