Potential and Energy

Energy from Potential

U = qV

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

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 VV = 6\ \text{V}
Charge at point PThe diagram marks the charge and point, not a free-text voltage.+2 Csource+4 Ctest

Multiply by charge

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

U=qVU = qV

Compute the energy

Multiplying 4 coulombs by 6 volts gives 24 joules.

U=4 C⋅6 V=24 JU = 4\ \text{C}\cdot 6\ \text{V} = 24\ \text{J}
Charge at point PThe diagram marks the charge and point, not a free-text voltage.+2 Csource+4 Ctest

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.

qVU2 C6 V12 J4 C6 V24 J6 C6 V36 J\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}
Charge at point PThe middle table row is the checked diagram.+2 Csource+4 Ctest

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.

qVU4 C3 V12 J4 C6 V24 J4 C9 V36 J\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}
Charge at point PThe middle table row is the checked diagram.+2 Csource+4 Ctest
electrostatics Potential times charge gives energy.