Calculate electrostatic forces and combine perpendicular or opposing contributions.
Method and worked examples
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.
Example 1
Two charges +2.00μC and −3.00μC are 0.300m apart. Use k=8.99×109.
F=r2k∣q1q2∣=0.599N. The force is attractive; each charge experiences this magnitude.
Example 2
A charge experiences 3.00N east and 4.00N north. Find resultant.
F=√32+42=5.00N, directed arctan(34)=53.1∘ north of east.
Watch out:The pair forces have equal magnitudes by Newton’s third law; accelerations can differ.
1. Coulomb forces and vector addition | Year 12 Physics | Ascent Arcade