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# Dimensions of $\dfrac{1}{{{\mu _o}{\varepsilon _o}}}$, where symbols have their usual meaning?

Last updated date: 24th Jul 2024
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Hint:Let us first get some idea about Dimensions. The dimension of a mathematical space (or object) is specified informally in physics and mathematics as the minimum number of coordinates required to specify some point within it.

Let us talk about permittivity. The absolute permittivity, also known as permittivity and denoted by the Greek letter $\varepsilon$ (epsilon), is a measure of a dielectric's electric polarizability in electromagnetism. A material with a high permittivity polarises more in response to an applied electric field than one with a low permittivity, allowing it to store more energy.

The relative permittivity ${\varepsilon _r}$, which is the ratio of the absolute permittivity $\varepsilon$ and the vacuum permittivity ${\varepsilon _0}$ is often used to represent permittivity.
${\varepsilon _r} = \dfrac{\varepsilon }{{{\varepsilon _0}}}$
Let's get some idea about permeability. Permeability is the measure of magnetization that a material obtains in response to an applied magnetic field in electromagnetism. The (italicised) Greek letter $\mu$ is commonly used to denote permeability. Oliver Heaviside invented the word in September 1885. Magnetic reluctivity is the reciprocal of permeability.

The permeability constant ${\mu _0}$ also known as the magnetic constant or permeability of free space. ${\varepsilon _0}$ is permittivity of vacuum and its dimension will be [${M^{ - 1}}{L^{ - 3}}{T^4}{I^2}$]. Vacuum Permeability is given by ${\mu _0} = 4\pi \times {10^{ - 7}}N/{A^2}$ and its dimensions will be [$ML{T^{ - 2}}{I^{ - 2}}$]. Therefore, dimensions for $\dfrac{1}{{{\mu _0}{\varepsilon _0}}}$ will be,
$\dfrac{1}{{[{M^{ - 1}}{L^{ - 3}}{T^4}{I^2}] \times [ML{T^{ - 2}}{I^{ - 2}}]}} = [{L^2}{T^{ - 2}}]$

Hence, the dimensions of $\dfrac{1}{{{\mu _o}{\varepsilon _o}}}$ is $[{L^2}{T^{ - 2}}]$.

Note:Dimensioning is used to provide a complete and accurate definition of an entity. Only one interpretation is needed to create the part with a full set of dimensions. These rules should be followed while dimensioning. Accuracy: the values must be right.