The integral therefore becomes . The potential due to a point charge is proportional to the inverse of the distance from the point charge. To find the potential due to a collection of charges, we use the principle of superposition and add the potentials due to the individual charges. Because the potential is a scalar, and not a vector, we just have to add numbers. Each surface corresponds to a different fixed value of the potential.
Equipotential lines are lines connecting points of the same potential.
They often appear on field line diagrams. Equipotential lines are always perpendicular to field lines, and therefore perpendicular to the force experienced by a charge in the field. Field lines and equipotential lines for a constant field between two charged plates are shown below. Field lines and equipotential lines for a positive point charge are shown below. The force on the electron is the Coulomb force between the proton and the electron.