Electric Potential of a Point Charge

Formula

Description

Electric potential is the electrostatic potential energy per unit charge at a distance r from a point charge. Unlike the field, potential is a scalar and falls off as 1/r rather than 1/r². The difference in potential between two points is the voltage that drives current. Setting the potential to a reference defines the voltage that appears across capacitors and in any electrostatic problem.

Variables

• V — Electric potential (V)
• q — Source charge (C)
• r — Distance from the charge (m)
• kₑ — Coulomb constant

Practical Notes

Potential is taken as zero at infinity. The work to bring a charge q′ from infinity to this point is q′·V. The electric field is the negative gradient of potential, E = −dV/dr.