# The relation between Electric Field and Electric Potential

Tags:
1. Jul 1, 2016

### ItsAnshumaan

1. The problem statement, all variables and given/known data

The electric field and the electric potential at a point are E and V respectively.
(a) If E=0, V must be 0
(b) If V=0, E must be 0
(c) If E≠0, V cannot be 0
(d) If V≠0, E cannot be 0

2. Relevant equations

E = V/d

3. The attempt at a solution

I basically substituted the value of E and V as 0 in respective cases, but ended up getting (a) and (b) as true. I know this is a very fundamental question, but I just can't figure it out.

2. Jul 1, 2016

### cnh1995

In your question, V is the absolute potential at the given point while electric field E=potential difference/d.

3. Jul 1, 2016

### SammyS

Staff Emeritus
Does any one of them have to be true?

It looks like there are pairs of them which are logically equivalent.

4. Jul 1, 2016

Te electric field E and electric potential V are two separate functions. Although the potential depends on the electric field, they are not proportional and the potential depends on the integral of the electric field over a path. The forum rules don't allow simply giving the answer, but the answer is quite simple. @SammyS The pairs are not logically equivalent. The equation the OP presents that E=V/d does have precise proportionality between E and V, but this equation is very misleading because it does not apply in general. It is for the special case of an ideal capacitor and E is the uniform electric field between the plates and V is the voltage drop across the plates. The equation really does not apply here, and the capacitor equation does not give V at any location between the plates where the E field is present. Although it looks like the right equation, it is totally irrelevant to this problem.

Last edited: Jul 1, 2016
5. Jul 1, 2016

### SammyS

Staff Emeritus
Are you saying that there is no pair that are not logically equivalent?

From a pure logic point of view.

(P implies Q) is logically equivalent to ((not Q) implies (not P)) .

It appears to me that we can find cases where one of these statements is the contrapositive of another.

6. Jul 1, 2016