Field Vector Superposition Audit - Electric Fields, Electrostatics & Capacitors Step by Step

At one point, each source contributes a field vector. The net field is the signed vector sum, not a new independent arrow.

electrostatics Add field contributions at the same point, with right and left recorded as signed directions.

Example

At one point, each source contributes a field vector. The net field is the signed vector sum, not a new independent arrow. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Pick one point before adding

Superposition is local. Put the sample point P between two sources, then write the field contribution at that same point from each source.

\text{add field contributions at the same point }P

Record the left-source field

The left source contributes a field of 4 newtons per coulomb to the right at point P.

E_{\text{left at }P} = 4\ \text{N/C}\quad \text{right}

Record the right-source field with sign

The right source contributes 3 newtons per coulomb to the left. Use a negative sign for left on this line, so the contribution is -3 newtons per coulomb.

E_{\text{right at }P} = -3\ \text{N/C}

Add signed field contributions

Right is positive in this ledger. The net field is 4 plus -3, which leaves 1 newton per coulomb to the right.

E_{\text{net}} = 4\ \text{N/C} + -3\ \text{N/C} = 1\ \text{N/C}

Three rows reveal the cancellation boundary

Hold the left contribution at 4 newtons per coulomb and scan three right-source contributions. The middle row is the drawn case; the last row reaches the exact cancellation boundary.

\begin{array}{c|c|c}E_{\text{left}}&E_{\text{right}}&E_{\text{net}}\\4\ \text{N/C}&-1\ \text{N/C}&3\ \text{N/C}\\4\ \text{N/C}&-3\ \text{N/C}&1\ \text{N/C}\\4\ \text{N/C}&-4\ \text{N/C}&0\ \text{N/C}\\\end{array}