Potential as Energy per Charge - Electric Fields & Electrostatics Step by Step

Electric potential is an energy budget per coulomb, measured relative to a chosen reference.

Example

Electric potential is an energy budget per coulomb, measured relative to a chosen reference. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

State the energy difference

Measure potential against a chosen reference. Moving this 3 coulomb positive charge to point P takes 18 joules of energy.

q = 3\ \text{C}\qquad U = 18\ \text{J}

Potential is energy per charge

Electric potential tells the energy difference for each coulomb of charge at the point.

V = \frac{U}{q}

Compute joules per coulomb

Divide 18 joules by 3 coulombs. The potential difference is 6 volts.

V = \frac{18\ \text{J}}{3\ \text{C}} = 6\ \text{V}

More energy gives more volts at fixed charge

Hold the charge at 3 coulombs. The diagram shows the middle row; increasing the energy budget increases joules per coulomb.

\begin{array}{c|c|c}U&q&V\\9\ \text{J}&3\ \text{C}&3\ \text{V}\\18\ \text{J}&3\ \text{C}&6\ \text{V}\\27\ \text{J}&3\ \text{C}&9\ \text{V}\\\end{array}

More charge lowers joules per coulomb

Now hold the energy budget at 18 joules. More charge divides the same energy into more coulombs, so the potential is smaller.

\begin{array}{c|c|c}U&q&V\\18\ \text{J}&2\ \text{C}&9\ \text{V}\\18\ \text{J}&3\ \text{C}&6\ \text{V}\\18\ \text{J}&6\ \text{C}&3\ \text{V}\\\end{array}

electrostatics Potential compares energy to charge.