Question

The dimensional formula of $\frac{1}{2}{\epsilon }_0{E}^2$ is (E = electric field)

• A. $\left[ML{T}^{-1}\right]$
• B. $\left[M{L}^2{T}^{-2}\right]$
• C. $\left[M{L}^{-1}{T}^{-2}\right]$
• D. $\left[M{L}^2{T}^{-1}\right]$

Answer 1

Answer: (C)

$\frac{1}{2}{\epsilon }_0{E}^2=$ Energy density
$=\frac{E}{V}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^3\right]}$
$=\left[M{L}^{-1}{T}^{-2}\right]$