Electrostatic Potential energy and Electrostatic potential

Consider a positive charge q kept fixed at the origin, producing an electric field in the surrounding space. To bring a small positive test charge q0 from a reference point (conventionally taken at infinity, where the field and potential are both zero) to some point P against the repulsive force exerted by q, an external agent must do positive work, since the electric force resists this motion. This work done by the external agent is stored as electrostatic potential energy of the two-charge configuration, in exact analogy with the way work done lifting a mass against gravity is stored as gravitational potential energy. Because the electrostatic force is conservative, this work -- and hence the potential energy -- depends only on the starting and ending positions of the test charge, never on the particular path taken between them. Dividing the work required per unit of test charge moved defines a new, purely scalar quantity called the electrostatic potential V at point P: V = W/q0 (work done bringing a unit positive test charge from infinity to P). Electric potential is measured in volts (1 V = 1 J/C) and, like the electric field, depends only on the source charge configuration, not on whatever test charge is used t …