# What is Coulomb's law?

Aug 1, 2014

Coulomb's Law states that the force between the two objects is directly proportional to the charge of each object and inversely proportional to the square of the distance between them.

In chemistry, we usually write the formula as

$F = k \frac{{q}_{1} {q}_{2}}{r} ^ 2$

where $F$ is the force, ${q}_{1}$ and ${q}_{2}$ are the charges, $r$ is the distance between them, and $k$ is a proportionality constant.

Chemists most often use the law in a modified form to calculate the energy of interaction $E$ between the charges.

$E = k \frac{{q}_{1} {q}_{2}}{r}$

When ${q}_{1}$ and ${q}_{2}$ are expressed as electronic charges, $k$ = 2.307 × 10⁻²⁸ J·m.

If the particles have opposite charges, like an electron and proton, then the energy $E$ is always negative.

The energy of interaction approaches zero when the particles get further apart from each other. The energy becomes more negative as they come closer to each other.

Example

Calculate the energy of an electron that is 52.9 pm from a proton.

Solution

E = k(q_1q_2)/r = 2.307 × 10^-28"J·m" × ((+1) × (-1))/(52.9 × 10^-12"m") = -4.36 × 10⁻¹⁸ J