Electric Field Strength (HL IB Physics)

• An electric field is a region of space in which an electric charge experiences a force
• The electric field strength at a point is defined as:

The force per unit charge experienced by a small positive test charge placed at that point

• The electric field strength can be calculated using the equation:

• Where:
  • E = electric field strength (N C⁻¹)
  • F = electric force on the charge (N)
  • q = magnitude of the charge (C)

• Note that the definition specifies that a positive test charge is used
• This sets a clear convention for the direction of an electric field, for example, in a field of strength :
  • A positive charge  experiences a force  in the direction of the field
  • A negative charge  experiences a force  in the opposite direction

• Hence, electric field strength is a vector quantity and is always directed:
  • Away from a positive charge
  • Towards a negative charge

Electric Field Strength due to a Point Charge

• 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, this can be written as

• Where k = Coulomb constant (N m² C^–2)
• A charged sphere acts the same as a point charge, with the same charge as the sphere, at the sphere's centre
  • Within the sphere, however, the electric field strength is zero

• This means that the electric field of a charged sphere, outside the sphere, is identical to that of a point charge

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
• 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

• The magnitude of the electric field strength in a uniform field between two charged parallel plates is defined as:

• Where:
  • E = electric field strength (V m⁻¹)
  • V = potential difference between the plates (V)
  • d = separation between the plates (m)

• Note: both units for electric field strength, V m⁻¹ and N C⁻¹, are equivalent 
• The equation shows:
  • The greater the voltage between the plates, the stronger the field
  • The greater the separation between the plates, the weaker the field

• This equation cannot be used to find the electric field strength around a point charge
  • This is because the field around a point charge is radial

• The electric field between two plates is directed:
  • From the positive plate (i.e. the one connected to the positive terminal)
  • To the negative plate (i.e. the one connected to the negative terminal)

Uniform Electric Field Between two Parallel Plates

The electric field strength between two charged parallel plates is the ratio of the potential difference and separation of the plates