Question

The dimension of $\left(\frac{1}{2}\right){\epsilon }_0{E}^2$ is (${\epsilon }_0$: permittivity of free space, Electric field)

• A. ${MLT}^{-1}$
• B. ${ML}^2{T}^{-2}$
• C. ${ML}^{-1}{T}^{-2}$
• D. ${ML}^2{T}^{-1}$

Answer 1

Answer: (C)

${ML}^{-1}{T}^{-2}$

Dimensional formula of permittivity of free space=$\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$

Dimensional formula of permittivity of electric field=$\left[M^1{L}^1{T}^{-3}{A}^{-1}\right]$

Dimensional formula of $\frac{1}{2}{ϵ}_0{E}^2$=$\left[M^1{L}^{-1}{T}^{-2}\right]$