4.14 Electric Force between Two Charges

• All charged particles produce an electric field around them
  • 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 force F_E between two charges as expressed by Coulomb's Law is given by the equation:

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 the separation of two charges doubles, the electrostatic force between them reduces to (½)² = ¼ of its original size
• ε₀ is a physical constant used to show the capability of a vacuum to permit electric fields

• If Q₁ and Q₂ are oppositely charged, then the electrostatic force F_E is negative
  • This can be interpreted as an attractive force between Q₁ and Q₂

• If Q₁ and Q₂ are the same charge, then the electrostatic force F_E is positive
  • This can be interpreted as a repulsive force between Q₁ and Q₂

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