Question

The dimensional formula of $\frac{1}{2} \varepsilon_{0} E^{2}$ is (E = electric field)

• A. $\left[ M L T ^{-1}\right]$
• 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)

$\frac{1}{2} \varepsilon_{0} E^{2}=$ Energy density
$=\frac{E}{V}=\frac{\left[M L^{2} T^{-2}\right]}{\left[L^{3}\right]}$
$=\left[ ML ^{-1} T ^{-2}\right]$