Dimensions of 1/(ε₀μ₀) , where symbols have their usual meanings, are:

The correct option is [L²T⁻²].

Step-by-step Explanation:

We know from electromagnetic theory that the speed of light in vacuum, denoted by $c$, is related to the permittivity of free space (${\epsilon }_0$) and the permeability of free space (${\mu }_0$) by the relation:

$c=\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}$

Squaring both sides of the equation, we obtain:

$c^2=\frac{1}{{\epsilon }_0{\mu }_0}$

From this relation, it is clear that the dimensions of the expression $\frac{1}{{\epsilon }_0{\mu }_0}$ must be identical to the dimensions of $c^2$ (the square of the speed of light).

Since speed $c$ has the dimensions of velocity:

$\left[c\right]=\left[{\mathrm{LT}}^{-1}\right]$

Squaring these dimensions to find the dimensions of $c^2$ gives:

$\left[c^2\right]={\left[{\mathrm{LT}}^{-1}\right]}^2=\left[L^2{T}^{-2}\right]$

Therefore, the dimensions of $\frac{1}{{\epsilon }_0{\mu }_0}$ are [L²T⁻²].