Electric Potential

Recall that energy methods utilizing quantities such as kinetic and potential energy can provide solutions to problems that would be very difficult to solve using Newton's second law. Electric potential is defined in terms of the work required to move a small positive test charge q₀ in the presence of an electrostatic force:

Definition: the electric potential difference V_B - V_A between two points A and B in a region of space that contains an electric field is the work per unit charge done against the field required to move a small positive test charge q₀ from point A to point B. In symbols:

The units of electric potential are Joules/Coulomb = Volt (V).

Notice that electric potential, like potential energy, is a scalar (not a vector!) quantity.

Special Case Formulas for Specific Electric Fields

Be careful when applying these formulas - they only apply to specific situations!

Uniform field:

where d is a displacement in the direction of the field E.

Point charge field:

where V is now interpreted as the absolute (relative to zero at infinity) potential.