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 for Nonuniform Fields

The calculus-savvy reader will have no difficulty generalizing the field- voltage relationship to the case of a varying field. The potential energy associated with a varying force is

so for electric fields we divide by q to find

Applying the fundamental theorem of calculus yields

Voltage associated with a point charge

Self-Check Show that you can recover the expression for the field of a point charge by evaluating the derivative E = -dV/dx.

Last Update: 2009-06-21