# 4.15 Electric Field due to a Point Charge

## 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

#### Worked example

Calculate the strength of the electric field at a distance of 2 m away from an electron, and state its direction.

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 × 1012
• 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

#### Exam Tip

Remember to square the distance in the electric field strength equation! Don't get this mixed up with the electric force between two charges equation, which has two charges (Q) in the equation, whilst the equation for E only has 1 Q, which is the one producing the electric field. ### Get unlimited access

to absolutely everything:

• Unlimited Revision Notes
• Topic Questions
• Past Papers 