Relative Permittivity Formula vs Pressure & Temperature

Introduction: Relative permittivity, also known as dielectric constant, is a fundamental material property that determines how an electric field interacts with a medium. In practical applications such as atmospheric propagation, sensors and capacitors, relative permittivity varies with environmental factors like pressure and temperature. Understanding this dependence is essential for accurate electromagnetic modeling and material characterization.

Relative Permittivity (Dielectric Constant) Formula

Definition: is a dimensionless quantity that indicates how much an electric field is reduced inside a material compared to free space. It describes the ability of a medium to store electrical energy when exposed to an electric field.

Formula: The equation for relative permittivity is as follows.

Where,

• ε = Absolute permittivity of the medium (F/m)
• ε0​ = Permittivity of free space, 8.854 x 10^-12 F/m

Relation with Capacitance:

Where,

• C = Capacitance with dielectric

• Co = Capacitance in vacuum

• Higher εr means greater polarization and more electric energy storage

Relation of relative permittivity with altitude and pressure

Permittivity decreases as altitude increases since there is significant drop in air pressure and humidity with increase in altitude. This change alters propagation properties of radio waves.

• For gases, relative permittivity is directly proportional to pressure.

Reason : Increasing pressure increases molecular density

At low pressures :

Where, Where ‘k’ is a proportionality constant.

• Air permittivity slightly increases with atmospheric pressure

Relation of relative permittivity with temperature

In gases,

• Increase in temperature, molecules move faster
• Relative permittivity decreases

In liquids and solids,

• Increasing temperature generally decreases εr

Approximate linear relation is as follows.

Where,

• α = temperature coefficient of permittivity
• To = Referemce temperature

Effect on Electomagnetic Wave propagation:

• Higher the εr, lower is the wave velocity

Summary: Relative permittivity quantifies how a material responds to an electric field and is defined as the ratio of material permittivity to free-space permittivity. In gases, it increases with pressure and decreases with temperature, while in solids and liquids it generally decreases with rising temperature due to reduced dipole alignment.