# Understanding Equipotential Lines and their relationship with Electric Field Lines

1. Feb 25, 2010

### lee9786

I understand the concept of electric field lines but don't understand the interaction with the equipotential lines. I understand that along each equipotential line/surface that there is no change in potential energy. I also understand the field lines need to cross perpendicularly with the equipotential lines. I don't know why though. Could anyone offer some insight on these equipotential lines. I really don't get why they're even there.

2. Feb 25, 2010

### Stonebridge

Re: Understanding Equipotential Lines and their relationship with Electric Field Line

What you say about these lines is correct. As for why they are there, they help visualise an electric field. The lines of force do too, but in a different way.
The equipotentials are very similar to isotherms or isobars on a map. Lines that connect all points with the same value of something are very useful.

3. Feb 25, 2010

### Born2bwire

Re: Understanding Equipotential Lines and their relationship with Electric Field Line

The electric field is related to the potential by the gradient of the potential. Thus, the electric field points along the direction of greatest change in the potential which would be normal to any equipotential lines. Going along with the iso-XXX trend, the equipotential lines are like the topographical lines in a map that dictate lines of constant altitude. The closer the lines are, the greater the change in elevation and the change in elevation, the slope of the land, lies normal to the topographical lines. In the same exact way, the electric field is akin to the change in the altitude on the map.

4. Feb 25, 2010

### Studiot

Re: Understanding Equipotential Lines and their relationship with Electric Field Line

I think you are putting the cart before the horse.

At any point in an electric field a test charge must be at some potential.
Some nearby point will be at the same potential.
So we must be able to draw a line between such points.
This, of couse, is an equipotential line.

Now the question is

Why should this line be perpedicular to the line of electric force passing through the same point?

Well the electric field line is a measure of the mechanical force experienced by the test charge. This force is directed along the line.

Now suppose we want to move the test charge along an equipotential line.
This means there is no change of potential energy so no work is done on the charge.

This can only happen if the charge is moved perpendicular to the force exerted upon it by the electric field line.

Therefore the equipotential line must be perpendicular to the field line.