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Coulomb's Law

Source lecture(s): SC134 Lec1-2

Intuition

Point charges exert central forces scaling as \(1/r^2\)—the electrical analog of Newton's law of gravitation.

Formal Definition

\[\vec{F}_{12} = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r_{12}^2}\hat{r}_{12}\]

Mathematical Formulation

Coulomb constant: \(k_e = 1/(4\pi\varepsilon_0) \approx 8.99\times10^9\,\text{N·m}^2/\text{C}^2\).

Derivation

Experimental law from Coulomb's torsion balance; vector form follows from superposition.

Worked Example

For \(q_1=+3\,\mu\)C, \(q_2=-1.5\,\mu\)C at \(12\,\text{cm}\): \(F\approx 2.8\,\text{N}\).

Common Mistakes

  • Forgetting the vector direction.
  • Using \(\varepsilon_0\) without \(4\pi\).

Quiz

Q1. What direction does force act for like charges?

Answer

Repulsive, along line joining them.