# What is the Vacuum Permittivity (Electric Constant)?

## Answer #1

The **electric constant** (or vacuum permittivity) is a physical constant and is notated as \( \varepsilon_0 \) (pronounced: "epsilon zero"). It has the following value:

**Value of the vacuum permittivity**

The unit of \(\varepsilon_0\) is for example

*ampere-second per voltmeter*or*farad per meter*:**Unit of the vacuum permittivity**Formula anchor $$ \begin{align} \frac{\mathrm{As}}{\mathrm{Vm}} ~=~ \frac{\mathrm{F}}{\mathrm{m}} ~=~ \frac{\mathrm{A}^2\,\mathrm{s}^4}{\mathrm{kg}\,\mathrm{m}^3} \end{align} $$The vacuum permittivity appears in equations that have to do with electric fields. For example, in Coulomb's law or in the wave equation for electromagnetic waves.

In our universe, the vacuum permittivity determines how strongly electric charges are allowed to attract or repel each other.

The vacuum permittivity, together with the vacuum permeability \(\mu_0\) (magnetic constant), determines how large the speed of light \(c\) should be in vacuum:

**Vacuum permittivity is the reciprocal of the vacuum permeability and speed of light squared**Formula anchor $$ \begin{align} c ~=~ \sqrt{\frac{1}{\mu_0 \, \varepsilon_0}} \end{align} $$Vacuum permittivity \(\varepsilon_0\) specifies how easy / hard it is for electric fields to

*penetrate*the vacuum. Permittivity \(\varepsilon\) of water, for example, is about eighty times the permittivity of vacuum: \( \varepsilon = 80 \cdot \varepsilon_0 \). Here the factor \( \varepsilon_{\text r} = 80 \) is called**relative permittivity**.

**How can the vacuum permittivity be determined experimentally?**:

The vacuum permittivity \( \varepsilon_0 \) can be determined experimentally, for example, with a so-called **Coulomb's torsion balance**. Similar to the Eötvös gravitational balance, it exploits the torque exerted on each other by two known charges \( q_1 \) and \( q_2 \).

From the experimentally determined electric force \( F_{\text e} \) between the two charges, the value of the vacuum permittivity can be found using Coulomb's law:

**Coulomb's law rearranged for vacuum permittivity**