Parallel Plate Capacitor (AQA A Level Physics): Revision Note

Relative permittivity & dielectric constant

• Permittivity is the measure of how easy it is to generate an electric field in a certain material

• The relative permittivity ${\epsilon }_r$ 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:

${\epsilon }_r=\frac{\epsilon }{{\epsilon }_0}$

• Where:

  • ${\epsilon }_r$ = relative permittivity

  • $\epsilon$ = permittivity of a material (F m^-1)

  • ${\epsilon }_0$ = 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

Dielectric action in a capacitor

• 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 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, which decreases the potential difference between the plates

  • Therefore, the capacitance of the plates increases

• The capacitance of a capacitor can also be written in terms of the relative permittivity:

$C=\frac{A{\epsilon }_0{\epsilon }_r}{d}$

• Where:

  • $C$ = capacitance (F)

  • $A$ = cross-sectional area of the plates (m²)

  • $d$ = separation of the plates (m)

  • ${\epsilon }_r$ = relative permittivity of the dielectric between the plates

  • ${\epsilon }_0$ = permittivity of free space (F m^-1)

• Capacitor plates are generally square, so if they have a length $L$ on all sides, then their cross-sectional area is $L^2$