Plate Field Gap Ratio Scan - Capacitors & Stored Charge Step by Step

Parallel plates turn voltage and separation into an exact uniform field, with voltage and gap scanned separately. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A plate gap turns voltage into field

Use ideal parallel plates with voltage 12 volts across a gap of 3 metres. The checked uniform field is 4 newtons per coulomb.

E=\frac{V}{d}

Fixed gap: voltage raises the field

Hold the plate gap fixed. More voltage across the same distance raises the field in equal steps.

\begin{array}{c|c|c}V&d&E\\6\ \text{V}&3\ \text{m}&2\ \text{N/C}\\12\ \text{V}&3\ \text{m}&4\ \text{N/C}\\18\ \text{V}&3\ \text{m}&6\ \text{N/C}\\\end{array}

Fixed voltage: wider gaps lower the field

Now hold voltage fixed. Spreading the same voltage across a wider gap lowers the field, so the denominator matters as much as the voltage numerator.

\begin{array}{c|c|c}V&d&E\\12\ \text{V}&2\ \text{m}&6\ \text{N/C}\\12\ \text{V}&3\ \text{m}&4\ \text{N/C}\\12\ \text{V}&4\ \text{m}&3\ \text{N/C}\\\end{array}

The arrows are the middle table row

The diagram arrows all carry the same field value because the ideal central field is uniform. The displayed arrow value and the table's middle field value are the same checked quantity.

E=4\ \text{N/C}