How Does Force Between Two Charges Vary With Distance?

The electrical force ($F$) between two point charges varies inversely as the square of the distance ($r^2$) between them.

Mathematically, this is written as: $F \propto \frac{1}{r^2}$

In 1785, the French physicist Charles-Augustin de Coulomb published his famous law. It states two things:

1. The force of attraction (or repulsion) is directly proportional to the magnitude of the two charges ($q_1$ and $q_2$). If the charges are massive, the force is massive.
2. The force is inversely proportional to the square of the distance ($r$) between their centers.

The Full Formula: $F = k \frac{|q_1 \cdot q_2|}{r^2}$ (Where $k$ is Coulomb's constant)..

Because the distance is 'squared' in the denominator, the force drops off incredibly fast as you move away:

• If you Double (2x) the distance between two electrons, the repulsive force doesn't become half; it becomes One-Fourth (1/4th) as strong ($1/2^2$).
• If you move the charges Three times (3x) further apart, the force becomes One-Ninth (1/9th) as strong ($1/3^2$).
• Conversely, if you bring them extremely close together (half the distance), the force becomes 4 times stronger!