Force as gradient of potential function

[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?

 

[Redbelly98]

Yes, you're right.

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

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

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

 

[JP O'Donnell]

thanks.

 

[Alia Al-Hajri]

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

 

[Per Oni]

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

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.

 

[Alia Al-Hajri]

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.

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!