by The dimensions of permittivity for vacuum or air can be determined by the use of Coulomb’s Law. The permittivity of free space is the ability of electric fields to pass through a vacuum . It’s value is (8.854\times10^{-12})F/m or (8.854\times10^{-12}C^2N{-1}m^{-2}).
To determine the dimensions of permittivity we can use Coulomb’s Law.
The force between two charged objects is
![\[F=\frac{q_1q_2}{4\pi \epsilon_o r^2}\]](https://physicsqanda.com/wp-content/ql-cache/quicklatex.com-b357cbdfc719d12f8704fb5f83994f8e_l3.png "Rendered by QuickLaTeX.com")
![\[\epsilon_o =\frac{q_1q_2}{4pi F r^2}\]](https://physicsqanda.com/wp-content/ql-cache/quicklatex.com-65ec395ceafe35200975301d17a1358c_l3.png "Rendered by QuickLaTeX.com")
The dimensions of force are:
![\[[F]=[MLT^{-2}]\]](https://physicsqanda.com/wp-content/ql-cache/quicklatex.com-494036d32383a980fe4fa9c3e8ce7af0_l3.png "Rendered by QuickLaTeX.com")
The dimensions of charge are:
![\[[q]=[AT]\]](https://physicsqanda.com/wp-content/ql-cache/quicklatex.com-aba33f241d5b056b7a814cff30c06684_l3.png "Rendered by QuickLaTeX.com")
Here
is dimensionless quantity.substituting the dimensions is the above formula.
![\[\epsilon_o =\frac{[AT]^2}{[MLT^{-2}] [L ] ^ 2}\]](https://physicsqanda.com/wp-content/ql-cache/quicklatex.com-b86d80db4b53b8d7c8fe3962657f98ea_l3.png "Rendered by QuickLaTeX.com")
![\[\boxed { \epsilon_o = [M^{ -1 } L ^ { - 3} T ^4 A^2 ] }\]](https://physicsqanda.com/wp-content/ql-cache/quicklatex.com-8f18e38b2c9e21784ac7e1c3a47d6f8f_l3.png "Rendered by QuickLaTeX.com")
