The dimension of (1/2)ε₀E² are (ε₀ : permittivity of free space, E : electric field )

The correct option is [ML⁻¹T⁻²].

Step-by-step Explanation:

The expression $\frac{1}{2}{\epsilon }_0{E}^2$ represents the electrostatic energy density (energy per unit volume) in an electric field.

$\text{Energy Density}=\frac{\text{Energy}}{\text{Volume}}$

To find its dimensions, we can use the dimensional formulas of energy and volume:

1. Dimensional formula of energy:
$\left[\text{Energy}\right]=\left[{\text{ML}}^2{\text{T}}^{-2}\right]$

2. Dimensional formula of volume:
$\left[\text{Volume}\right]=\left[{\text{L}}^3\right]$

Substituting these dimensions into the formula for energy density:
$\left[\text{Energy Density}\right]=\frac{\left[{\text{ML}}^2{\text{T}}^{-2}\right]}{\left[{\text{L}}^3\right]}$

$\left[\text{Energy Density}\right]=\left[{\text{ML}}^{2-3}{\text{T}}^{-2}\right]$

$\left[\text{Energy Density}\right]=\left[{\text{ML}}^{-1}{\text{T}}^{-2}\right]$

Therefore, the dimensions of $\frac{1}{2}{\epsilon }_0{E}^2$ are [ML⁻¹T⁻²].