How this calculator works
Potential is energy per unit test charge. A point-charge potential falls as inverse distance with zero set at infinity. Several sources contribute scalar potentials that can be added directly, unlike vector electric fields. Difference modes use delta U = q delta V and do not depend on the chosen zero of potential. The dielectric must be uniform for the point-source expressions used here.
Formula
V = kq/(epsilonr r); Vsystem = (k/epsilonr) sum(q_i/r_i). Delta V = delta U/q and delta U = q delta V.
Worked example
A 1 microcoulomb source at 1 m in vacuum has potential 8987.55 V. If a -3 C test charge gains 12 J of potential energy, its potential difference is -4 V.
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Frequently asked questions
Can the potential be negative?
Yes. With zero at infinity, negative sources give negative potentials.
Does zero potential imply zero field?
No. Opposite sources can cancel scalar potential while their vector fields add.
Is energy change the work done by the electric field?
Electric-field work is the negative of potential energy change. A slow external mover does work equal to delta U.