4.15 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

Step 1: Write out the equation for electric field strength

Step 2: Substitute quantities for charge, distance and permittivity of free space

• • The charge on an electron Q = –1.6 × 10^–19 C
  • The distance r = 2 m
  • Permittivity of free space ε₀ = 8.85 × 10^–12
  • Therefore:

E = = –3.6 × 10^–10 N C^–1

Step 3: State the direction of the field

• • The negative sign indicates the electric field is directed towards the electron