Why Is Potential Constant When E-Field Is 0?

[indigojoker]

if the E-field is zero in a region of space, why i the potential always a constant?

For example:

$$V=-\int E dl$$

if E = 0, then wouldn't the potential automatically be zero?

 

[fikus]

From Maxwell equations for stationary fields: $$\nabla \times E = 0$$
it follows that E is gradient of some field. So we write $$E = -\nabla \phi$$.
You see that if you change phi for a constant results the same field E.
All it counts are the differences in phi. So potential can also be zero.