Superposition Audits

Field Vector Superposition Audit

add signed field arrows

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

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.

add field contributions at the same point P\text{add field contributions at the same point }P
Two sources, one pointBoth sources bracket the same sample point P.P+4 Cleft+3 Cright

Record the left-source field

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

Eleft at P=4 N/CrightE_{\text{left at }P} = 4\ \text{N/C}\quad \text{right}
Left contributionThe rightward field arrow is the left-source contribution.P+4 Cleft+3 Cright4 N/C

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.

Eright at P=−3 N/CE_{\text{right at }P} = -3\ \text{N/C}
Right contributionThe leftward field arrow is the right-source contribution.P+4 Cleft+3 Cright4 N/C3 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.

Enet=4 N/C+−3 N/C=1 N/CE_{\text{net}} = 4\ \text{N/C} + -3\ \text{N/C} = 1\ \text{N/C}
Net fieldThe net arrow is shorter because opposite field contributions subtract.P+4 Cleft+3 Cright1 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.

EleftErightEnet4 N/C−1 N/C3 N/C4 N/C−3 N/C1 N/C4 N/C−4 N/C0 N/C\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}
Net fieldThe middle table row is the checked diagram.P+4 Cleft+3 Cright1 N/C
electrostatics Add field contributions at the same point, with right and left recorded as signed directions.