Electric potential

Line integral of the electric field

Electric potential, also known as the electrostatic potential or electric field potential, is a field of scalar quantities through space, often denoted with the letter φ {\displaystyle \varphi } or V {\displaystyle V} , that gives, for each point in space, the electric potential energy per unit of electric charge that a point charge would have if it was located at that point: at every point, a particle of charge q particle {\displaystyle q_{\text{particle}}} would have the electric potential energy U particle when at the point = q particle V point {\displaystyle U_{\text{particle when at the point}}=q_{\text{particle}}\,V_{\text{point}}} . The difference in electric potential energy U, U = U B − U A {\displaystyle U=U_{B}-U_{A}} , that a charged particle of charge q {\displaystyle q} would have between two points A {\displaystyle A} and B {\displaystyle B} in a static electric field, equals q {\displaystyle q} times the difference V B − V A {\displaystyle V_{B}-V_{A}} of the electric potentials at A and B: U B − U A = q × ( V B − V A) {\displaystyle U_{B}-U_{A}=q\times (V_{B}-V_{A})} . More precisely, electric potential is the amount of work needed to move a test charge from a reference point to a specific point in a static electric field, normalized to a unit of charge.

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