Energy from Potential - Electric Fields, Electrostatics & Capacitors Step by Step

Once a potential difference is known, multiplying by charge gives the electric potential energy difference.

electrostatics Potential times charge gives energy.

Example

Once a potential difference is known, multiplying by charge gives the electric potential energy difference. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Start with potential per charge

At point P, the potential difference from the reference is 6 volts. That means 6 joules per coulomb.

V = 6\ \text{V}

Multiply by charge

Place a 4 coulomb positive charge at the same point. It has 4 copies of the energy-per-coulomb amount.

U = qV

Compute the energy

Multiplying 4 coulombs by 6 volts gives 24 joules.

U = 4\ \text{C}\cdot 6\ \text{V} = 24\ \text{J}

More charge stores more energy at fixed voltage

Hold the potential difference at 6 volts. The diagram shows the middle row; energy grows directly with charge.

\begin{array}{c|c|c}q&V&U\\2\ \text{C}&6\ \text{V}&12\ \text{J}\\4\ \text{C}&6\ \text{V}&24\ \text{J}\\6\ \text{C}&6\ \text{V}&36\ \text{J}\\\end{array}

More volts means more energy at fixed charge

Now hold the charge at 4 coulombs. A larger potential difference means more joules for the same charge.

\begin{array}{c|c|c}q&V&U\\4\ \text{C}&3\ \text{V}&12\ \text{J}\\4\ \text{C}&6\ \text{V}&24\ \text{J}\\4\ \text{C}&9\ \text{V}&36\ \text{J}\\\end{array}