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The dimension of $\frac{1}{2}\varepsilon_0E^2$, where $\varepsilon_0$ is permittivity of free space and E is electric field, is
A
$MLT^{-1}$
B
$ML^2T^{-2}$
C
$ML^{-1}T^{-2}$
D
$ML^2T^{-1}$
Detailed Solution
$\frac{1}{2}\varepsilon_0E^2$ is the energy stored per unit volume in an electric field, i.e., the energy density.
Energy density = $\frac{\text{energy}}{\text{volume}}$
Dimensions of energy = $[ML^2T^{-2}]$; dimensions of volume = $[L^3]$
Dimensions of energy density = $\frac{[ML^2T^{-2}]}{[L^3]}$
$= [ML^{-1}T^{-2}]$
Energy density = $\frac{\text{energy}}{\text{volume}}$
Dimensions of energy = $[ML^2T^{-2}]$; dimensions of volume = $[L^3]$
Dimensions of energy density = $\frac{[ML^2T^{-2}]}{[L^3]}$
$= [ML^{-1}T^{-2}]$