Question

The dimension of $\dfrac{1}{2}\varepsilon_0 E^2$ is

Hint:

The expression $1/2 \epsilon_0 E^2$ is the formula for energy density (Energy/Volume).

Answer 1

The quantity $\frac{1}{2}\varepsilon_0 E^2$ represents the energy density of an electric field, which is energy stored per unit volume.

Dimension of Energy $[E] = ML^2T^{-2}$. Dimension of Volume $[V] = L^3$.

Thus, the dimension of energy density is $\frac{[E]}{[V]} = \frac{ML^2T^{-2}}{L^3} = ML^{-1}T^{-2}$.

Therefore, the dimension of $\frac{1}{2}\varepsilon_0 E^2$ is $ML^{-1}T^{-2}$.