Does Zero Electric Potential Necessarily Imply Zero Electric Field?

[lockedup]

Homework Statement

If V = 0 at a point in space, must E = 0? If E = 0 at some point, must V = 0 at that point?

Homework Equations

The Attempt at a Solution

V = 0 means there is no PE at that point is zero. However, the PE may have been converted to KE which would require a non-zero E field.

Am I in the ballpark? Now, I just need the second part...

 

[rl.bhat]

What is the relation between E and V?