11.3.2 Dielectric Materials

• Permittivity is the measure of how easy it is to generate an electric field in a certain material
• The relativity permittivity ε_r is sometimes known as the dielectric constant
• For a given material, it is defined as:

The ratio of the permittivity of a material to the permittivity of free space

• This can be expressed as:

  

• Where:
  • ε_r = relative permittivity
  • ε = permittivity of a material (F m^-1)
  • ε₀ = permittivity of free space (F m^-1)

• The relative permittivity has no units because it is a ratio of two values with the same unit

Step 1: Write down the relative permittivity equation

Step 2: Rearrange for permittivity of the material ε

ε = ε_rε₀

Step 3: Substitute in the values

ε = (4.5 × 10¹¹) × (8.85 × 10^-12) = 3.9825 = 4 F m^-1

Dielectric Material Effects on Capacitance

• A dielectric material separates the two conductive metal plates of a capacitor
  • The dielectric itself is an insulator
• When the polar molecules in a dielectric align with the applied electric field from the plates, they each produce their own electric field
  • This electric field opposes the electric field from the plates

The electric field of the polar molecules opposes that of the electric field produced by the parallel plates

• The larger the opposing electric field from the polar molecules in the dielectric, the larger the permittivity
  • In other words, the permittivity is how well the polar molecules in a dielectric align with an applied electric field

• The opposing electric field reduces the overall electric field
• For an isolated capacitor, this decreases the potential difference between the plates
  • Therefore, the charge remains constant and the capacitance of the plates increases

• For a capacitor attached to a power supply, the potential difference between the plates is unchanged (with a dielectric)
  
  • Therefore, the charge on one of the plates increases and the capacitance of the plates also increase
• The capacitance of a capacitor can also be written in terms of the relative permittivity:

• Where:
  • C = capacitance (F)
  • A = cross-sectional area of the plates (m²)
  • d = separation of the plates (m)
  • ε_r = relative permittivity of the dielectric between the plates
  • ε₀ = permittivity of free space (F m⁻¹)

• When the electrical permittivity of the dielectric is known, a simpler form of this equation can be used:

• Where:
  • C = Capacitance (F)
  • A = cross-sectional area of the plates (m²)
  • d = separation of the plates (m)
  • ε = permittivity of the dielectric between the plates (F m⁻¹)

A parallel plate capacitor consists of conductive plates each with area A, a distance d apart and a dielectric ε between them

• Capacitor plates are generally square, therefore if they have a length L on all sides then their cross-sectional area is L²