# Relation between electric potential energy and electric field

1. May 31, 2013

### Pushpam Singh

Please explain the relation between electric potential energy and electric field in detail.

2. May 31, 2013

### d.3vil

component of the electric field at
a given point in space is equal to minus the local gradient of the electric potential in that direction...

3. Jun 2, 2013

### tannerbk

Because ∇ x E = 0, it is possible to write the electric field as a gradient of some scalar. This is true for any vector whose line integral around a close loop is 0 (path indepdendence). Because the line integral is path indepdendent we define V(r) = - ∫ E . dl . It is then easy to derive E = -∇V. I think these two equations provide the best insight into the relation between the electric field and the electric potential. Remember that in the definition of the electric potential there is a choice of reference point that is arbitrary. Thus any two V's differing only in reference point correspond to the same E.

4. Jun 2, 2013

### Staff: Mentor

Please do not ask questions like that, see https://www.physicsforums.com/blog.php?b=3588 [Broken] for details.

Last edited by a moderator: May 6, 2017