Physics · Ch 1 — Electrostatics
Superposition principle
Superposition principle
Coulomb's law by itself only describes the interaction between exactly two point charges; when more than two charges are present, Coulomb's law alone cannot say what net force one particular charge experiences from all the others simultaneously. The superposition principle fills this gap: the total force acting on any given charge equals the vector sum of the separate forces exerted on it by every other charge in the system, computed one pair at a time using Coulomb's law, and then added as vectors. For a system of n charges q1, q2, ..., qn, the total force on q1 due to all the rest is F_tot,1 = F12 + F13 + F14 + ... + F1n, where each F1i = k(q1 qi / r1i^2) r-hat-i1 is the ordinary two-body Coulomb force from charge qi alone, computed exactly as if the other charges were not present. This is the crucial physical content of superposition: the electrostatic force between any two charges is completely unaffected by the presence of other charges nearby -- each pairwise interaction is independent, and the net effect is simply their vector sum. Superposition and Coulomb's law together form the two foundational principles of electrostatics; without superposition, Coulomb's …
Worked out. Four equal charges q1 = q2 = q3 = q4 = +1 uC sit at four points on a circle of radius 1 m, and the question asks for the total force on q1 due to the other three. By the superposition principle the total force is the vector sum F_tot on q1 = F12 + F13 + F14. Charges q2 and q4 are equidistant from q1 so their individual force magnitudes are equal (though pointing in different directions), while q3 sits farther away (across the circle) so F13 is weaker than F12 and F14. Resolving all three forces into x and y components, the y-components of F12 and F14 cancel by the symmetry of the arrangement while their x-components add together with the x-component of F13, giving a net resultant force of 8.61x1 …
What this figure shows. A diagram shows the resultant of several individual point-charge force (or field) vectors being combined tip-to-tail or by component addition into one net vector, using unequal arrow lengths to represent the unequal magnitudes contributed by charges at different distances. It is the visual companion to the superposition principle: rather than one single formula, the net effect at any point is built up by drawing every pairwise contribution separately and then adding the vectors according to the ordinary rules of vector addi …