18.1.3 Electric Field Strength

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

• Where:
  • E = electric field strength (V m^-1)
  • ΔV = potential difference between the plates (V)
  • Δd = 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

• Remember 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

Step 1: Write down the known values

Potential difference, ΔV = 7.9 kV = 7.9 × 10³ V

Distance between plates, Δd = 3.5 cm = 3.5 × 10^-2 m

Charge, Q = 2.6 × 10^-15 C

Step 2: Calculate the electric field strength between the parallel plates

Step 3: Write out the equation for electric force on a charged particle

F = QE

Step 4: Substitute electric field strength and charge into electric force equation

F = QE = (2.6 × 10^-15) × (2.257 × 10⁵) = 5.87 × 10^-10 N = 5.9 × 10^-10 N (2 s.f.)

• 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:

• 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/r²

• This is 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

Step 1: Write down the known values

Electric field strength, E = 1.5 × 10⁵ V m^-1

Radius of sphere, r = 15 / 2 = 7.5 cm = 7.5 × 10^-2 m

Step 2: Write out the equation for electric field strength

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)