Surfaces which connect points that are at the same absolute potential, or voltage, are called equipotential surfaces. In the diagram of the point charge shown in the previous example, two equipotential surfaces were labeled, A and B. Notice that equipotential surfaces meet field lines at right angles. The closer together two equipotential surfaces are to each other, the more rapid the change in voltage. This indicates a stronger electric field which is shown in the second diagram below by the fact that the field lines are grouped more closely together on the left side where the equipotential surfaces are also more closely clustered together.
Note that the electric field strength, E, can be measured in either the units V/m, or equivalently, in the unit N/C.
N/C = V / d = (J/C) / m = [(Nm)/C] / m
= N/C Shown below are two more illustrations showing the relationships between field lines and equipotential surfaces. The image on the left shows two positive point charges of equal magnitude; while the image on the right shows two charges of equal magnitude but differing in sign. Note that the field lines (represented by vectors) meet every equipotential surface at right angles.
The following two graphs compare the voltage around a positively charged conducting sphere and the electric field for the same positively charged conducting sphere under electrostatic conditions. Note that the electric field strength (E ∝ 1/r ^{2}) drops off more rapidly than does the voltage (V ∝ 1/r). Also notice that within a conducting sphere, the voltage remains constant in contrast to the fact that no electric field exists.


For a conducting sphere, V = kQ/r

For a conducting sphere, E = kQ/r^{2}

Remember that the electric field strength, E, is a vector quantity. You are required to state both its magnitude and its direction to completely describe it at any given location. If you are ever asked to calculate the net electric field in 2dimensions, you should first take the x and ycomponents of each field, add the components to determine the net E_{x} and net Ey, and then calculate the resultant field and its direction. Voltage, on the other hand, is a scalar quantity and can be added directly without considering components or directions.
Let's work through the next examples to show you the difference in these two field properties. In each set of diagrams, compare the charge configuration diagram and voltage diagram to determine the requested information for each midpoint. The charges are assumed to be a distance "2r" apart. That os, the midpoint is located a distance "r" from each point charge. 