#### Electric Potential from a Point Charge

The potential a distance r from a point charge Q is given by:

V = kQ/r

As with electric field, potential can be represented by a picture. We draw equipotential surfaces that connect points of the same potential, although in two dimensions these surfaces just look like lines.

For a 2-D representation of the equipotentials from a point charge, the equipotentials are circles centered on the charge. The difference in potential between neighboring equipotentials is constant, so the equipotentials get further apart as you go further from the charge. In 3-D the equipotentials are actually spherical shells.

#### Electric Potential in a Uniform Field

Potential energy in a uniform field is U = qEd, so potential is:

V = U/q = Ed

d here is some distance moved parallel to the field, and is measured from some convenient reference point.

More important is the potential difference, which increases as you move in the opposite direction of the field:

DV = EDd

Even more generally, DV = -E · Dr

#### Equipotentials

• Equipotential surfaces are always perpendicular to field lines.

• No work is required to move a charge along an equipotential.

• Equipotentials connect points of the same potential. They are similar to contour lines on a topographical map, which connect points of the same elevation, and to isotherms (lines of constant temperature) on a weather map.