Question

Which of the following is the dimensional formula for electric polarisation ?

• A. $\left[M^0{L}^{-2}{T}^1{I}^1\right]$
• B. $\left[M^1{L}^{-2}{T}^1{I}^{-1}\right]$
• C. $\left[M^0{L}^{-1}{T}^1{I}^1\right]$
• D. $\left[M^{-1}{L}^{-2}{T}^1{I}^1\right]$

Answer 1

Answer: (A)

Electric polarisation $(P)$ is given by $P={\epsilon }_0\chi E$
where, $E$ is electric field and $\chi$ is electric susceptibility and it is dimensionless quantity, Dimensional formula of $P=$ Dimensional formula of $\left({\epsilon }_0\right)\times$ Dimensional formula of $E$
$=[M^{-1}{L}^{-3}{T}^4{I}^2][ML{T}^{-3}{I}^{-1}]=[M^0{L}^{-2}{T}^1{I}^1]$