Distinguish a field null from a zero potential

Define the source and measurement boundary

For two positive point charges on a line, fields point away from each source. Between them the contributions oppose; outside them they point in the same direction. Therefore the finite cancellation point lies between the sources, not beyond an endpoint. Source positions themselves are singular and cannot be substituted as candidate nulls.

Derive the quantitative comparison

Let the left charge be +1 nC at x=0 and the right be +a nC at x=d. Equating magnitudes gives 1/x²=a/(d−x)². Both distances are positive inside the interval, so d−x=√a x and x=d/(1+√a). The stronger source lies farther from the null. The field is zero there, but V=k×10⁻⁹[1/x+a/(d−x)] remains positive relative to infinity.

Test an alternative before claiming identification

Compare a separate +1/−1 nC pair at the same positions. At its midpoint the signed scalar potentials cancel, yet both field contributions point from the positive source toward the negative one. Their sum is 8k×10⁻⁹/d². Zero field, zero potential, zero total charge and zero potential energy are different statements. The potential reference matters for V=0; adding a constant changes that statement but not any force or potential difference. A field null also does not by itself prove stable equilibrium for arbitrary three-dimensional displacements.

Worked original case

For a=9 and d=2 m, the field null is x=2/(1+3)=.5 m. Its distances from the sources are .5 and 1.5 m. The source-field magnitudes match because 1/.5²=9/1.5²=4; the potential contributions are both positive.

Investigation

Hold separation at 2 m and compare right charges 1,5,9 nC. Predict the direction of null motion before checking. Draw the separate equal-and-opposite midpoint case and use vector arrows and scalar signs to explain its contrasting cancellations.

Changed-case practice

Sources and evidence boundary

Original teaching, numerical cases and diagrams checked 30 October 2026 against the relevant primary textbook explanation. No textbook exercise, image or passage is reproduced. These are bounded synthetic records, not observed apparatus. No charging, wiring, capacitor handling, medical application or safety certification is requested. Preserve first predictions, contrasting settings and critiques in the course evidence workspace; public feedback is not independent mastery or performed laboratory time.