A LevelPhysicsCIERevision Notes18. Electric Fields18.4 Electric Field of a Point ChargeElectric Field Strength of a Point Charge

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First teaching 2023

First exams 2025

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

Revision Note

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Ann H

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Ann H

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Electric Field of a Point Charge

  • The electric field strength at a point describes how strong or weak an electric field is at that point
  • The electric field strength E at a distance r due to a point charge Q in free space is defined by:

 

E space equals fraction numerator space Q over denominator 4 straight pi straight epsilon subscript 0 r squared end fraction

  • Where:
    • Q = the charge producing the 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 is not constant
    • As the distance from the charge, r  increases, E decreases by a factor of 1 over r squared

  • This is also an inverse square law relationship with distance
  • This means the field strength decreases by a factor of four when the distance is doubled
  • Note: this equation is only for the field strength around a point charge since it produces a radial field

 

  • 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

Worked example

A metal sphere of diameter 15 cm is negatively charged. The electric field strength at the surface of the sphere is 1.5 × 105 V m-1.

Determine the total surface charge of the sphere.

Answer:

 Step 1: Write down the known values

  • Electric field strength, E = 1.5 × 105 V m-1
  • Radius of sphere, r = 15 over 2 = 7.5 cm = 7.5 × 10-2 m

Step 2: Write out the equation for electric field strength

 

E space equals space fraction numerator Q over denominator 4 straight pi straight epsilon subscript 0 r squared end fraction

 

Step 3: Rearrange for charge Q

Q = 4πε0Er2

Step 4: Substitute in values

Q = (4π × 8.85 × 10-12) × (1.5 × 105) × (7.5 × 10-2)2 = 9.38 × 10-8 C = 94 nC (2 s.f)

Exam Tip

Remember to always square the distance!

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    Ann H

    Author: Ann H

    Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students no matter their schooling or background.