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