Electric Force Between Two Point Charges (Cambridge (CIE) A Level Physics)

Point charge approximation

• When calculating the force between two charges, air is treated as a vacuum

  • This is why the permittivity of free space ε₀ is used

• For a point outside a spherical conductor, the charge of the sphere may be considered to be a point charge at its centre

  • A uniform spherical conductor is one where its charge is distributed evenly

• The electric field lines around a spherical conductor are therefore identical to those around a point charge

  • An example of a spherical conductor is a charged sphere

• The field lines are radial and their direction depends on the charge of the sphere

  • If the spherical conductor is positively charged, the field lines are directed away from the centre of the sphere

  • If the spherical conductor is negatively charged, the field lines are directed towards the centre of the sphere

Electric field lines around a uniform spherical conductor are identical to those on a point charge

Coulomb's law

• All charged particles generate an electric field

  • This field exerts a force on charged particles which are nearby

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

  The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them

• This electric force can be calculated using the expression:

• Where:

  • F = electric force between two charges (N)

  • Q₁, Q₂ = magnitudes of the charges (C)

  • r = distance between the centres of the two charges (m)

  • ε₀ = permittivity of free space

Electrostatic attraction between two charges

The attractive electric force F_E between two point charges +Q and −Q with a separation of r is defined by Coulomb’s law

• The constant 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

  • All other materials have a higher permittivity ε > ε₀

  • ε is a measure of the resistance offered by a material in creating an electric field within it

• Sometimes Coulomb's law may be written as

• Where is the Coulomb constant

• The value of k depends on the material between the charges

  • In a vacuum, k = 8.99 × 10⁹ N m² C^–2

Repulsive & attractive forces 

• Unlike the gravitational force between two masses which is only attractive, electric forces can be:

  • attractive (the charges move closer together)

  • repulsive (the charges move further apart)

Opposite charges attract, like charges repel

• Between two charges of the same type: 

  • The product Q₁Q₂ is positive, so the electrostatic force is positive

  • A positive force means the charges experience repulsion

• For two opposite charges:

  • The product Q₁Q₂ is negative, so the electrostatic force is negative

  • A negative force means the charges experience attraction