Relation Cross-Scans

Energy Charge Potential Two-Factor Scan

U = qV

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

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 Vq=4 CV=6\ \text{V}\qquad q=4\ \text{C}
Energy from potentialThe charge is drawn while the voltage is pinned in math.P+2 Csource+4 Ctest

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=qVU=qV

Compute total 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}
Energy from potentialThe drawn charge is the middle row of both scans.P+2 Csource+4 Ctest

Scan charge at fixed voltage

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

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}

Scan voltage at fixed charge

Hold charge fixed at 4 coulombs. More volts 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}
Energy from potentialThe final row connects volts to joules through charge.P+2 Csource+4 Ctest
electrostatics Read total energy as charge multiplied by energy per charge.