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BlogWhat is Permittivity? Meaning, Definition, Formula, SI Unit & Relation to Dielectric Constant

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What is Permittivity? Meaning, Definition, Formula, SI Unit & Relation to Dielectric Constant

Edited by:Aakash Digital

5 min read • Updated on Sep 16 2026, 11:32 PM IST

Quick summary

This guide explains permittivity's meaning, formula, and SI unit, along with the free space permittivity value, relative permittivity, dielectric constant, and how it differs from permeability.

Table of contents

Permittivity Explained: Formula, Unit & Free Space Value

Two charges placed in air attract or repel each other with a certain force. Move the same charges into water, keeping the distance unchanged, and the force drops to about one-eightieth of its earlier value. The medium is clearly doing something. That property of the medium is called permittivity.

What is Permittivity? Meaning and Definition

Permittivity is the measure of how much a medium resists the formation of an electric field inside it, or how easily it allows electric field lines to pass through. It is represented by the symbol ε (epsilon).
A medium with high permittivity weakens the electric field of a charge placed inside it, because its molecules polarise and set up an opposing field. Water has high permittivity, which is why it reduces the electrostatic force so strongly.

Permittivity Formula

Permittivity enters physics through Coulomb's law. The force between two point charges in a medium is:
F = (1 / 4πε) × (q₁q₂ / r²)
In vacuum, this becomes:
F = (1 / 4πε₀) × (q₁q₂ / r²)
Rearranging gives the permittivity formula:
ε = q₁q₂ / (4πFr²)
Permittivity also appears in Gauss's law, written as Φ = q(enclosed) / ε₀, and in the capacitance of a parallel plate capacitor, C = ε₀A/d.

SI Unit of Permittivity and Its Dimensional Formula

The SI unit of permittivity is farad per metre (F/m). It is also written as C² N⁻¹ m⁻² or C² kg⁻¹ m⁻³ s², and all of these are equivalent.
The dimensional formula of permittivity is:
[M⁻¹ L⁻³ T⁴ A²]
This is also the permittivity of free space dimensional formula, since ε₀ and ε have the same dimensions. You can verify it by rearranging Coulomb's law, where charge carries the dimensions [AT].

What is the Value of Permittivity of Free Space?

The permittivity of free space value, also called the electric constant or vacuum permittivity, is:
ε₀ = 8.854 × 10⁻¹² F/m (approximately 8.85 × 10⁻¹² C² N⁻¹ m⁻²)
This value comes from the Coulomb constant used in numericals:
1 / 4πε₀ = 9 × 10⁹ N m² C⁻²
Free space here means vacuum. Air has permittivity very close to that of vacuum, with a relative permittivity of about 1.0006, so ε₀ is used for air in almost all school and entrance exam problems.

Relative Permittivity and Dielectric Constant

Relative permittivity is the ratio of the permittivity of a medium to the permittivity of free space:

εᵣ = ε / ε₀

This ratio is exactly what we call the dielectric constant (K) of the medium. So εᵣ and K mean the same thing. Being a ratio, it is a pure number with no unit and no dimensions.

Medium	Dielectric Constant (approximate)
Vacuum	1
Air	1.0006
Paper	3.7
Glass	5 to 10
Water	80
Barium titanate	above 1000

Two useful results follow from this ratio:

The force between charges in a medium becomes F(medium) = F(vacuum) / K. This is why the force in water falls to about 1/80 of its value in air.
Inserting a dielectric between capacitor plates increases capacitance K times, so C = Kε₀A/d. This is the reason capacitors are filled with dielectric material instead of air.

Permittivity vs Permeability

These two constants are often confused because their names sound similar and both describe a medium. The difference lies in which field they belong to.

Basis	Permittivity (ε)	Permeability (μ)
Related field	Electric field	Magnetic field
Meaning	How the medium responds to an electric field	How the medium supports a magnetic field
Free space value	8.854 × 10⁻¹² F/m	4π × 10⁻⁷ H/m
SI unit	farad per metre (F/m)	henry per metre (H/m)
Dimensional formula	[M⁻¹L⁻³T⁴A²]	[MLT⁻²A⁻²]
Appears in	Coulomb's law, Gauss's law	Biot-Savart law, Ampere's law

The two constants meet in one of the most important results in physics. The speed of light in vacuum is:

c = 1 / √(μ₀ε₀)

Substituting the values gives 3 × 10⁸ m/s, which is how Maxwell established that light is an electromagnetic wave.

Why Permittivity Matters in Your Syllabus

Permittivity runs through the whole of Electrostatics. It decides the force in Coulomb's law, the flux in Gauss's law, the field of a charged sheet or sphere, and the capacitance of every capacitor you study. Questions from this topic usually take one of three forms: finding a force or field in a medium, comparing capacitance before and after a dielectric is inserted, or identifying the correct dimensional formula. Learning the value of ε₀ and its dimensions properly therefore saves you time across several chapters.

Solved Examples

Example 1: Two charges of 2 μC and 3 μC are placed 10 cm apart in vacuum. Find the force between them. F = (9 × 10⁹ × 2 × 10⁻⁶ × 3 × 10⁻⁶) / (0.1)² F = (9 × 10⁹ × 6 × 10⁻¹²) / 0.01 = 5.4 N
Example 2: If the same charges are placed in a medium of dielectric constant 4, what is the new force? F(medium) = 5.4 / 4 = 1.35 N
Example 3: A capacitor of capacitance 5 μF in air is filled with a dielectric of K = 6. Find its new capacitance. C = K × C₀ = 6 × 5 = 30 μF

Conclusion

Permittivity tells you how a medium responds to an electric field, and its free space value of 8.854 × 10⁻¹² F/m appears throughout electrostatics. Relative permittivity is simply the dielectric constant, so the same number that divides the Coulomb force also multiplies the capacitance. Keeping the dimensional formula and the value of 1/4πε₀ ready will help you solve most numericals from this topic quickly.