Electric Field due to a Point Charge (Edexcel International A Level Physics)

Electric Field due to a Point Charge

• The electric field strength describes how strong or weak an electric field is at that point

• A point charge produces a radial field

  • A charge sphere also acts like a point charge

• The electric field strength E at a distance r due to a point charge Q in free space is defined by:

• 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)

• This equation shows:

  • Electric field strength in a radial field is not constant

  • As the distance from the charge r increases, E decreases by a factor of 1/r²

• This is an inverse square law relationship with distance

  • This means the field strength E decreases by a factor of four when the distance r is doubled

• Note: this equation is only for the field strength around a point charge since it produces a radial field

Positive and negative point charges and the direction of the electric field lines 

• The electric field strength is a vector Its direction is the same as the electric field lines

  • 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

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

  • The only difference is, gravitational field lines are always towards the mass, whilst electric field lines can be towards or away from the point charge

• The graph of E against r for a charge is:

The electric field strength E has a 1/r² relationship

• The key features of this graph are:

  • The values for E are all positive

  • As r increases, E against r follows a 1/r² relation (inverse square law)

  • The area under this graph is the change in electric potential ΔV

  • The graph has a steep decline as r increases