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Equipotential Lines (curves)

Once we envision what an electric field looks like using a field map we know somethng about the direction of the field and the strength of the field but very little about the electric potential of the field at different points.  For this information we need to create a series of lines (curves actually) that represent the amount of the electric potential at a given region.

potential difference to line

The animation to the left shows that it takes the same amount of work to pull a charge to one spot on the curve as it does to pull it out to a different spot on the curve.  That means that the work done per unit of charge (electric potential) is also the same.

The work done was 10J on 1C so the potential difference is 10J/C or 10 volts.
The animation to the left shows that no matter where the charge is dragged along that curve, the electric potential is the same.  We call that curve an equipotential line since no matter where you go on the curve the electric potential is equal.
This animation shows that as the charge crosses from one equipotential line to the next, we change the electric potential from 0 volts initially to 10 volts and then to 20 volts.  Comparing the electric potential from one line to the next gives us the concept of electrical potential difference.  The potential difference from the starting point to the farthest point in this case is 20 volts while the potential difference from the first line to the second is 10 volts.  It is simply a matter of taking the difference between the potential at one point and the potential at another point.

When we draw in the electric field lines (lines of force) and the equipotential lines on the same picture we find that the equipotential lines will always cross the field lines at right angles to each other. 

It is important to note that electric field lines have a defined direction, the direction of the force on a positve test charge.  The equipotential lines have no direction at all.