6.3.3 Electric Field Strength

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

The electrostatic force per unit positive charge acting on the charge at that point

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

• Where:
  • E = electric field strength (N C⁻¹)
  • F = electrostatic force on the charge (N)
  • Q = charge (C)

• It is important to use a positive test charge in this definition, as this determines the direction of the electric field
• The electric field strength is a vector quantity, it is always directed:
  • Away from a positive charge
  • Towards a negative charge

• 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: the electric field strength is now also defined by the units V m⁻¹
• 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 (since this would be a radial field)
• The direction of the electric field is from the plate connected to the positive terminal of the cell to the plate connected to the negative terminal

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

• Note: if one of the parallel plates is earthed, it has a voltage of 0 V

Derivation of Electric Field Strength Between Plates

• When two points in an electric field have a different potential, there is a potential difference between them
  • To move a charge across that potential difference, work needs to be done
  • Two parallel plates with a potential difference ΔV across them create a uniform electric field

The work done on the charge depends on the electric force and the distance between the plates

• Potential difference is defined as the energy, W, transferred per unit charge, Q, this can also be written as:

• Therefore, the work done in transferring the charge is equal to:

• Where:
• W = work done (J)
• F = force (N)
• d = distance (m)

• Equate the expressions for work done:

• Since  the electric field strength between the plates can be written as:

• • Potential difference, V = 7.9 kV = 7.9 × 10³ V
  • Distance between plates, d = 3.5 cm = 3.5 × 10⁻² m
  • Charge, Q = 2.6 × 10⁻¹⁵ C

Step 4: Substitute the values into the electric force equation

= 5.869 × 10⁻¹⁰ N

• • The magnitude of the electric force acting on this charged particle is 5.9 × 10⁻¹⁰ N