# Force as gradient of potential function

1. Nov 5, 2008

### JP O'Donnell

Hi.

Is it possible for two separate points on an equipotential surface to have two different values for the force field?

eg, point A and point B lie on an equipotential surface, but the equipotential surface spacing is much denser at A than at B - so the force field at A as the gradient of the potential must be greater than that at B?

Is this right?

2. Nov 5, 2008

### Redbelly98

Staff Emeritus
Yes, you're right.

A good example is to think about a dipole, and the line (really a surface) that runs halfway between them:

Code (Text):

O
|
<-------+------->
|
O

The electric field changes as one moves along the horizontal line, and has a maximum when you are halfway between the charges.

3. Nov 5, 2008

### JP O'Donnell

thanks.

4. Apr 19, 2011

### Alia Al-Hajri

Thanks allot....but can anyone gives more examples for me please..

5. Apr 20, 2011

### Per Oni

What about a charged metal needle? At the sharp point E is a lot higher then in the middle. In general any surface having the smaller radius has the higher density of field lines. Mind you higher local density doesn't equate to higher energy, this is so because the potential is equal.

6. Apr 21, 2011

### Alia Al-Hajri

Oh' ...Thank you..I really get the idea

I used to think that the surface area anything is a direct match with the density of field lines

So, That is not true!!!