Electrostatic Potential and Capacitance

The work done by an electrostatic

The work done by an electrostatic field in moving a charge depends only on the initial and final points, not on the path. Work done by an external for

The electrostatic potential at a point

The electrostatic potential at a point is the work done in bringing a unit positive charge without acceleration from infinity to that point. Potential

For a point charge Q at

For a point charge Q at distance r, V(r) = Q/(4πε0r). This is valid for any sign of Q, with infinity taken as the zero potential reference.

For an electric dipole with moment

For an electric dipole with moment p, the potential at a distant point is V = (1/4πε0)(p·r̂)/r², valid for r much larger than dipole size; it is exact

The total potential is the algebraic

The total potential is the algebraic sum of potentials due to individual charges: V = (1/4πε0)(q1/r1P + q2/r2P + ... + qn/rnP).