How Do You Use Coulomb's Law (F = kq1q2/r²)?

Coulomb's law calculates the magnitude of the electrostatic force between two point charges. Substitute both charges in coulombs and their separation in metres, then determine the force direction from whether the charges attract or repel.

This is part of D.2 Electric and magnetic fields and applies to both SL and HL.

The Method

For force magnitude, use

$$F = k\frac{|q_1q_2|}{r^2}$$

where:

• $F$ is the electrostatic force in newtons (N)
• $k = 8.99 \times 10^9\ \text{N m}^2\text{C}^{-2}$

The absolute value gives the magnitude. Use the charge signs separately to identify the direction.

Convert prefixes before substituting: $1\ \mu\text{C} = 1 \times 10^{-6}\ \text{C}$ and $1\ \text{nC} = 1 \times 10^{-9}\ \text{C}$.

Coulomb's law directly applies to point charges. Spherically symmetric charged bodies may be treated as point charges when their size is small compared with their separation; use the centre-to-centre distance. In a system containing more than two charges, calculate each force separately and add the forces as vectors. Do not add force magnitudes unless all forces act along the same direction.

Worked Example

Two point charges, $+2.0\ \mu\text{C}$ and $-3.0\ \mu\text{C}$, are separated by $0.20\ \text{m}$.

$$F=(8.99\times10^9)\frac{|(2.0\times10^{-6})(-3.0\times10^{-6})|}{(0.20)^2}$$ $$F=1.35\ \text{N}$$

Because the charges have opposite signs, the force is attractive. Each charge experiences a $1.35\ \text{N}$ force toward the other charge, consistent with Newton's third law. The two forces are equal in magnitude and opposite in direction; they do not cancel because they act on different bodies.

A common misconception is to use $r$, rather than $r^2$, in the denominator. Doubling the separation reduces the force to one quarter because Coulomb's law is an inverse-square law.

Exam Technique

For a Calculate question, show the equation, SI conversions, substitution, and final value. State “attractive” or “repulsive” when direction is required, and remember that $r$ is the separation between the centres of the charged bodies. If a vector direction is requested, define a positive axis and attach the appropriate sign to the force component.