AP® Physics C: Electricity and Magnetism · Unit 8 · Topic 8.1
Superposition of Electric Forces
Superposition says the net electric force on a charge from several other charges is just the vector sum of the separate Coulomb forces each one would exert alone. No charge's pull changes because other charges are also present.
Coulomb's law describes the force between exactly two point charges. Real situations usually have more than two, so superposition is the rule that lets you keep using Coulomb's law anyway: calculate the force each source charge exerts on your charge of interest as if the others weren't there, then add all those forces as vectors. Nothing about one pair's interaction depends on a third charge being nearby. The electric force is a two-body force at heart, and superposition is what promotes it into a tool for many-body problems.
The mechanism is always the same three steps: find the distance and direction from each source charge to the target, compute each force's magnitude with F = kq1q2/r2, then break each force into x and y components and add. Signs matter twice — once to tell you whether a given pair repels or attracts, and once when you assign plus or minus to components along your axes. Symmetry often does most of the work: charges placed symmetrically around a point can cancel certain components, leaving only one direction to compute.
This idea is the quiet partner behind everything else in the unit. The electric field at a point is just defined as the force per charge that superposition would produce there, so field calculations are superposition in disguise. Gauss's law later gives a shortcut for highly symmetric charge distributions, but it is built on the same underlying truth: every charge contributes independently, and total effects are sums of individual ones.
Key terms
- Superposition principle
- The net force on a charge from several others equals the vector sum of the individual Coulomb forces.
- Coulomb's law
- F = kq1q2/r2, giving the force magnitude between two point charges separated by distance r.
- Vector sum
- Combining forces by adding their components along chosen axes, not just their magnitudes.
- Point charge
- An idealized charge treated as existing at a single location with no size.
Watch it explained
- How it worksHow do three charges at the corners of a triangle each tug on a fourth one at the center?
- Worked exampleFind the net force on a +1 nC charge at the center of a square with +2 nC at three corners.
- Worked exampleFind the net force on a charge sitting midway between +6 nC and -6 nC that are 10 cm apart.
- Common mistakeWhy doesn't a nearby charge shield the one behind it from acting on a third charge?
Check yourself
End of topic.