• Permittivity is the measure of how easy it is to generate an electric field in a certain material
• The relativity permittivity?εr?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:
  • εr?= 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 = εrε0

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)
  • εr?= 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