Coulomb's Law
High-Yield Summary
- Coulomb's Law: Fe = kq1q2/r² — force ∝ product of charge magnitudes, ∝ 1/r². Doubling distance quarters the force, not halves it.
- Applies only to charges at rest. Opposite charges attract; like charges repel.
- With 3+ charges, find net force by vector-summing (superposition) the pairwise Coulomb forces.
- Electric field E = Fe/q = kQ/r² is a property of the source charge's surrounding space — exists whether or not a test charge is present.
- Electric field lines: point outward from + charges, inward toward − charges, never cross; density shows field strength.
Coulomb's Law and Electric Field
Fe = kq1q2/r² | E = Fe/q = kQ/r²
- Fe = Electrostatic force between two charges
- k = Coulomb's constant, 8.99×10⁹ N·m²/C² (= 1/4πε0)
- q1, q2 = Magnitudes of the two charges
- r = Distance between charges
- E = Electric field strength at a point
- Q = Source charge creating the field
- q = Test charge
- k = 1/(4πε0), where ε0 is the permittivity of free space.
Force vs. Field
| Electrostatic Force (Fe) | Electric Field (E) |
|---|---|
| Exists only between two specific charges | A property of a single source charge's surrounding space |
| Fe = kq1q2/r² | E = kQ/r² = Fe/q (force per unit test charge) |
| Requires both charges present | Exists even with no test charge there |
Common MCAT Trap
- The inverse-square dependence means distance changes are non-linear — doubling r drops force to 1/4, tripling drops it to 1/9.
- Electric field lines never cross — if a diagram shows crossing lines, it's depicting the field at two different times/sources, not one static field.
- Don't confuse Fe (a two-charge interaction) with E (a one-charge property of space) when a question swaps between them.
Quick Recall
If the distance between two charges triples, what happens to the force between them?
How do you find the net force on a charge from multiple other charges?