Using Coulomb’s Law

Coulomb's law describes the electrostatic force between two charged particles
It states that the force is directly proportional to the product of their charges and inversely proportional to the square of the distance between them
- $F_{coulombic} α (q_{1} \times q_{2})$
- $F_{coulombic} α \frac{1}{r^{2}}$
The formula for Coulomb's law is $F_{coulombic} = k \frac{q_{1} q_{2}}{r^{2}}$ , where:
- F_coulombic is the force between the charges in Newtons (N)
- k is Coulomb's constant (approximately 8.99 x 10⁹ N·m² C^-²)
- q₁ and q₂ are the value of the charges in Coulombs (C), which is the unit of measurement for charge
- r is the distance between the charges in meters (m)
The force is attractive for opposite charges and repulsive for like charges

Exam Tip

Always verify the units before any calculation. If the units are not consistent, make sure to perform any transformation before replacing the values into the Coulomb's Law formula

Worked example

Calculating the force that exists between a proton and an electron given the following information.

Charge of a proton = +1.602 x 10^-19 C
Charge of an electron = -1.602 x 10^-19 C
Distance between them = 1 x 10^-10 m

Answer

Step 1: Write down the values and the Coulomb's law formula

q₁ = +1.602 x 10^-19 C

q₂ = -1.602 x 10^-19 C

r = 1 x 10^-10 m

k = 8.99 x 10⁹ N·m² C^-²

$F_{coulombic} = k \frac{q_{1} q_{2}}{r^{2}}$

Step 2: Replace the value in the Coulomb’s Law

$F_{coulombic} = k \frac{q_{1} q_{2}}{r^{2}}$

$F_{coulombic} = 8.99 \times 10^{9} N m ² C^{- 2} \frac{(+ 1.602 \times 10^{- 19} C) (- 1.602 \times 10^{- 19} C)}{{(1 \times 10^{- 10} m)}^{2}}$

Step 3: Calculate the force.

F_coulombic = -2.31 x 10^-8 N

- The negative sign indicates an attractive force since proton and electron have opposite charges

Exam Tip

If the problem does not state the charge of the electron, you can find it in the AP Chemistry Equations and Constants that appear at the beginning of your examination. The charge of the proton has the same value but with a positive sign

Using Coulomb’s Law (College Board AP Chemistry)

Revision Note