Energy Charge Potential Two-Factor Scan - Electric Fields, Electrostatics & Capacitors Step by Step

Energy from potential is the reverse product. Charge and voltage each move the joule budget directly.

electrostatics Read total energy as charge multiplied by energy per charge.

Example

Energy from potential is the reverse product. Charge and voltage each move the joule budget directly. 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 volts and charge

At point P, the potential difference is 6 volts. A positive test charge of 4 coulombs samples that budget.

V=6\ \text{V}\qquad q=4\ \text{C}

Multiply charge by energy per charge

A volt is a joule per coulomb. Multiplying by charge converts the per-coulomb budget into total energy.

U=qV

Compute total energy

Multiplying 4 coulombs by 6 volts gives 24 joules.

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

Scan charge at fixed voltage

Hold voltage fixed at 6 volts. Three charge rows make the direct product visible.

\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}

Scan voltage at fixed charge

Hold charge fixed at 4 coulombs. More volts 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}