# What is Permittivity of Free Space?

Permittivity is an electric constant that measures the ability of a medium to store energy within the medium. If the medium is a vacuum then it is called the permittivity of free space/vacuum (𝜀o).

The value of (𝜀o) is measured by the formula -

$\varepsilon_{o} =\frac{1}{\mu _{o}c^{2}}$

Where c is the speed of light that has a defined value of 299792458 m/s and μ0 is called the magnetic constant ( commonly known as permeability of free space ) that has an approximate value of 4π × 10-7 N/A2. So εo can be expressed numerically as

$\varepsilon _{o}\approx \frac{1}{(4\pi \times 10^{-7}N/A^{2})(299792458m/s)^{2}}$

$\approx\;8.854\times 10^{-12} C^{2}N^{-1}m^{-2}$

## Units of Permittivity of Free Space

We all know from Coulomb's law that

$F=\frac{1}{4\pi \varepsilon _{o}}\frac{q_{1}q_{2}}{r^{2}}$

$\therefore \;\varepsilon _{o}=\frac{1}{4\pi F}\frac{q_{1}q_{2}}{r^{2}}$

We know that in the SI unit system the unit of charge is Coulomb (C), the unit of force is Newton (N), and the unit of distance is meter (m).

Therefore, in the SI unit system, the unit of permittivity of free space (𝜀o) is

$\frac{C^{2}}{Nm^{2}}=C^{2}N^{-1}m^{-2}$

## Dimension of Permittivity of Free Space

Similarly,

$Dimention \; of \;\varepsilon _{o}=\frac{\left [ Dimension\;of \;Charge \right ]^{2}}{\left [ Dimension\;of \; Force \right ]\times \left [ Dimension\;of \;Distance \right ]^{2}}$

$=\frac{\left [ I^{2}T^{2} \right ]}{\left [ MLT^{-2} \right ]\left [ L^{2} \right ]}$

$=\left [ M^{-1}L^{-3}T^{4}I^{2} \right ]$

## Relative & Absolute Permittivity

We know that when two charges are placed in a vacuum, then the effective force that is working between them is

$F_{vac}=\frac{1}{4\pi \varepsilon _{o}}\frac{q_{1}q_{2}}{r^{2}}$

And if the charges are placed in another medium instead of a vacuum, then the effective force that is working between them is

$F_{med}=\frac{1}{4\pi \varepsilon }\frac{q_{1}q_{2}}{r^{2}}$

Now

$\frac{F_{vac}}{F_{med}}=\frac{\varepsilon }{\varepsilon _{o}}=\varepsilon _{r}$

Here this 𝜀r is called relative permittivity, 𝜀  is called absolute permittivity/permittivity of the medium. and also 𝜀o is the permittivity of free space.

Read next: The Vector form of Coulomb's Law