Electric Field Strength of a Point Charge (CIE A Level Physics)

• The strength of an electric field due to a point charge decreases with the square of the distance
  • This is an inverse square law, similar to Coulomb's law

• Using Coulomb's law and the electric field strength equation this can be written as:

• Where:
  • Q = the point charge producing the radial electric field (C)
  • r = distance from the centre of the charge (m)
  • ε₀ = permittivity of free space (F m⁻¹)
• Here, q represents the magnitude of a small positive test charge

• This equation shows that in a radial electric field, the electric field strength E:
  • is not constant
  • follows an inverse square law with distance r

• This equation is analogous to the gravitational field strength around a point mass

Graph of field strength against distance for a positive charge

Electric field strength is zero inside a charged sphere and decreases with distance outside the sphere according to an inverse square law

Combining electric fields

• Both electric force and field strength are vector quantities
  • If the charge is negative, the E field strength is negative and points towards the centre of the charge
  • If the charge is positive, the E field strength is positive and points away from the centre of the charge

• Therefore, to find the electric force or field strength at a point due to multiple charges, each field can be combined by vector addition

Vector addition of electric field along the same line

For charges along the same line, the resultant field is the vector addition of the field due to both charges at a particular point

• For a point on the same line as two charges q₁ and q₂, with field strengths E₁ and E₂ respectively, the magnitude of the resultant field will be:
  • The sum of the fields, E₁ + E₂, if they are both in the same direction
  • The difference between the fields, E₁ − E₂, if they are in opposite directions

• The direction of the resultant field depends on:
  • The types of charge (positive or negative)
  • The magnitude of the charges

• For a point which makes a right-angled triangle with the charges, the resultant field can be determined using Pythagoras theorem

Vector addition of electric field components

For charges which make a right-angle triangle with point X, the resultant field is the vector addition of the field due to both charges using Pythagoras theorem