18.1.5 Electric Force Between Two Point Charges

• All charged particles produce an electric field around it
  • This field exerts a force on any other charged particle within range

• The electrostatic force between two charges is defined by Coulomb’s Law
  • Recall that the charge of a uniform spherical conductor can be considered as a point charge at its centre

• Coulomb’s Law states that:

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

• The Coulomb equation is defined as:

The electrostatic force between two charges is defined by Coulomb’s Law

• Where:
  • F_E = electrostatic force between two charges (N)
  • Q₁ and Q₂ = two point charges (C)
  • ε₀ = permittivity of free space
  • r = distance between the centre of the charges (m)

• The 1/r² relation is called the inverse square law
  • This means that when a charge is twice as far as away from another, the electrostatic force between them reduces by (½)² = ¼

• If there is a positive and negative charge, then the electrostatic force is negative, this can be interpreted as an attractive force
• If the charges are the same, the electrostatic force is positive, this can be interpreted as a repulsive force
• Since uniformly charged spheres can be considered as point charges, Coulomb’s law can be applied to find the electrostatic force between them as long as the separation is taken from the centre of both spheres

Step 1: Write down the known quantities

• • Distance, r = 2.0 mm =2.0 × 10^-3 m

The charge of one proton = +1.60 × 10^-19 C

An alpha particle (helium nucleus) has 2 protons

• • Charge of alpha particle, Q₁ = 2 × 1.60 × 10^-19 = +3.2 × 10^-19 C

The gold nucleus has 79 protons

• • Charge of gold nucleus, Q₂ = 79 × 1.60 × 10^-19 = +1.264 × 10^-17 C

Step 2: The electrostatic force between two point charges is given by Coulomb’s Law

Step 3: Substitute values into Coulomb's Law