Relation Cross-Scans

Potential Energy Charge Two-Factor Scan

V = U divided by q

Potential is energy per charge. This page scans energy and charge separately so volts stay tied to a quotient.

Example

Potential is energy per charge. Scanning energy and charge separately keeps volts from becoming an unexplained label. 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 an energy budget

Point P has an energy difference of 18 joules for a positive 3 coulomb test charge.

U=18 Jq=3 CU=18\ \text{J}\qquad q=3\ \text{C}
Potential from energyThe point and charge are drawn; energy stays pinned in the table.P+2 Csource+3 Ctest

Potential means joules per coulomb

Potential is the energy budget divided by the amount of charge used to sample that point.

V=UqV=\frac{U}{q}

Divide the energy by charge

Dividing 18 joules by 3 coulombs gives 6 volts.

V=18 J3 C=6 VV=\frac{18\ \text{J}}{3\ \text{C}}=6\ \text{V}
Potential from energyThe middle scan row is the rendered charge.P+2 Csource+3 Ctest

Scan energy at fixed charge

Hold charge fixed at 3 coulombs. More joules for the same charge means more volts.

UqV9 J3 C3 V18 J3 C6 V27 J3 C9 V\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}

Scan charge at fixed energy

Hold energy fixed at 18 joules. More charge divides the same budget into fewer joules per coulomb.

UqV18 J2 C9 V18 J3 C6 V18 J6 C3 V\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}
Potential from energyThe final table keeps energy and charge separate.P+2 Csource+3 Ctest
electrostatics Use separate rows for the energy numerator and the charge denominator.