5.1.5 Coulomb’s Law

• Any charged particle generates an electric field
  • This field exerts a force on any other charged particle within range

• The electrostatic force between two charges is defined by Coulomb’s Law, which states that:

The attractive or repulsive electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of their separation

• According to Coulomb's law, the electrostatic force between two point charges is calculated as follows:

• Where:
  • F = electrostatic force (N)
  • q₁, q₂ = magnitudes of the charges (C)
  • r = distance between the centres of the two charges (m)
  • k = Coulomb constant (N m² C^–2)

Attractive electrostatic force between two opposite charges

• Coulomb's constant is given by:

• The value of k depends on the material between the charges
  • In a vacuum, k = 8.99 × 10⁹ N m² C^–2

• ε₀ is the permittivity of free space
  • ε₀ = 8.85 × 10^–12 C² N^–1 m^–2 and refers to charges in a vacuum
  • The value of the permittivity of air is taken to be the same as ε₀
  • Any other material has a higher permittivity ε > ε₀
  • ε is a measure of the resistance offered by a material in creating an electric field within it

Repulsive & Attractive Forces 

• For like charges:
  • The product q₁q₂ is positive
  • F is positive
  • The charges repel each other

• For opposite charges:
  • The product q₁q₂ is negative
  • F is negative
  • The charges attract each other

Step 1: Write down the known quantities

• • Distance, r = 2.0 mm = 2.0 × 10^–3 m
  • Elementary charge, e = 1.60 × 10^–19 C (from the data booklet)

Note that you must convert the distance from millimetres (mm) into metres (m)

Step 2: Calculate the charges of the alpha particle and gold nucleus 

• • The elementary charge e (when taken to be positive) is the charge of a proton
  • An alpha particle (helium nucleus) has 2 protons
    • So its charge is:

q₁ = 2 × (1.60 × 10^–19) = 3.2 × 10^–19 C

• • A gold nucleus has 79 protons
    • So its charge is:

q₂ = 79 × (1.60 × 10^–19) = 1.264 × 10^–17 C

Step 3: Write down the equation to calculate the electrostatic force

Step 4: Substitute the numbers into the equation 

F = 9.1 × 10^–21 N