Coulomb forces and vector addition

For point charges in vacuum or approximately in air, the force magnitude is F=r2k∣q1q2∣​, with k=8.99×109Nm2C−2 when supplied. Use centre separation in metres and charges in coulombs. Like charges repel; unlike charges attract. Each interacting pair experiences equal-magnitude, opposite-direction forces, even if the charges differ.

For several charges, calculate each force on the selected charge separately and add the vectors. Subtract opposing collinear forces; use perpendicular components and Pythagoras for right-angle combinations. Doubling one charge doubles the force, while doubling separation reduces it to one quarter. The sign of a charge determines direction rather than a negative force magnitude.

Watch out: The pair forces have equal magnitudes by Newton’s third law; accelerations can differ.