Electricity and magnetism

Electric potential and voltage

Electric potential is electric potential energy per unit charge; a potential difference determines the change in energy as charge moves.

An electric field can be described through the force on a test charge or through energy. The potential $V$ at a point is electric potential energy $U$ per coulomb of positive charge. The potential difference between two points gives the work done by the electric force per unit charge as it moves between them.

Uniform field between parallel plates

Neglecting edge effects, the field between parallel plates separated by $d$ is approximately uniform: $E=|ΔV|/d$. It points from higher to lower potential. A charge $q$ changes its potential energy by $ΔU=qΔV$.

The potential of a point charge at distance $r$ in vacuum is $V=kQ/r$ when zero is chosen at infinity; potential is a scalar, so source contributions add algebraically. For example, how much does a $+3.0\,\mu$C charge gain in potential energy when moving from $20$ V to $80$ V? $\Delta U=q\Delta V=(3.0\times10^{-6})(60)=1.8\times10^{-4}$ J. A source must supply that energy to move the positive charge to higher potential when losses are absent.

Separating work from potential energy

Work by the electric force as a charge moves from $A$ to $B$ is $W_{A\to B}=-\Delta U=q(V_A-V_B)$. If a positive charge moves freely along the field, its potential energy decreases and the field does positive work. A negative charge feels force opposite the field, so track the charge sign rather than relying on the arrow alone. In an electrostatic field, work depends only on the endpoints, not the path.

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