18.5 Electric potential

Electric potential V at a point is work done per unit positive test charge bringing it from infinity, with zero potential at infinity.

Potential is scalar, so contributions add algebraically; electric field is a vector and requires direction.

A positive point charge gives positive potential, while a negative source gives negative potential relative to infinity.

Potential is not force per charge—that is field strength—and equal potential does not mean zero field everywhere.

Electric field strength points in the direction of decreasing electric potential; in one dimension E=−dV/dr.

The minus sign links field direction to potential fall. In a uniform field, the gradient is constant; near a point charge it changes with distance.

A potential drop of 20 V over 0.010 m in the field direction corresponds to E≈2000 N C⁻¹.

Electric field is not potential itself; a high potential region can have zero field if potential is locally constant.

For a point charge Q with zero potential at infinity, V=Q/(4πε₀r), with sign set by Q.

Potential is scalar, so potentials from several charges add algebraically. Use centre distance r and distinguish V from field strength.

Doubling distance from a positive point charge halves its positive potential.

Potential does not follow the inverse-square law—that applies to field magnitude, while point-charge potential follows 1/r.

A charge q at electric potential V has electric potential energy E_P=qV relative to the chosen zero; changes satisfy ∆E_P=q∆V.

Include the charge sign and reference level. A positive charge moving to lower V loses potential energy; a negative charge reverses that trend.

Moving a +2 μC charge through a 50 V rise increases potential energy by 1.0×10⁻⁴ J.

Potential is a property of the field location, whereas potential energy depends on both location and charge.