Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

# Voltage related to electric field

Voltage is potential energy per unit charge, and electric field is force per unit charge. We can therefore relate voltage and field if we start from the relationship between potential energy and force,

ΔPE = -Fd

[assuming constant force and motion parallel to the force],

and divide by charge,

ΔPE/q = -d/q

[assuming constant force and motion parallel to the force],

giving

ΔV = -Ed

[assuming constant field and motion parallel to the field].

In other words, the difference in voltage between two points equals the electric field strength multiplied by the distance between them. The interpretation is that a strong electric field is a region of space where the voltage is rapidly changing. By analogy, a steep hillside is a place on the map where the altitude is rapidly changing.

 Field generated by an electric eel

 Relating the units of electric field and voltage

Last Update: 2010-11-11