# Quick question reguarding electrical field lines.

1. Feb 18, 2006

### jrd007

Can anyone answer me a curious question. Why are electric field lines perpendicular to equipotential lines?

Is it because force and charge are inversly proportional or is there a more simple reason?

Thanks.

2. Feb 18, 2006

### dicerandom

There are a couple different ways to think about this. One is purely mathematical, the electric field is defined as being the change in potential:

$$\vec{E} = - \nabla V$$

This isn't terribly intuitive though. A more physical way of thinking about it is realising that equipotential surfaces are surfaces where the charge will have the same potential energy. The charge can move about on a given equipotential surface without changing its potential energy and therefore without needing to change its kinetic energy in order to conserve energy. When the charge leaves the equipotential surface its potential energy changes and therefore its kinetic energy must change, thus requiring a force.

3. Feb 19, 2006

### lightgrav

Why is the direction of gravity's Force radial (inward, downward)
while gravitational PE depends only on the coorsdinate "r"?
Places at the same potential are connected by paths of zero integrated Field, as in "zero Work", as in F perp. dx