Question

The dimension of permittivity (${\epsilon }_0$) are ______. Take $Q$ as the dimension of charge.

• A. $M^1{L}^{-2}{T}^{-2}{Q}^{-2}$
• B. $M^{-1}{L}^{-3}{T}^2{Q}^2$
• C. $M^{-1}{L}^2{T}^{-3}{Q}^{-1}$
• D. $M^{-1}{L}^3{T}^{-2}{Q}^{-2}$

Answer 1

Answer: (B)

$M^{-1}{L}^{-3}{T}^2{Q}^2$

We know that electrostatic force is given as:

$F=\frac{K{Q}^2}{r^2}$

We know that the dimension of force is $\left[F\right]=ML{T}^{-2}$

$\therefore ML{T}^{-2}=\frac{K{Q}^2}{r^2}\left[K\right]=M{L}^3{T}^{-2}{Q}^{-2}K=\frac{1}{4\pi {\epsilon }_o}\left[{\epsilon }_o\right]=M^{-1}{L}^{-3}{T}^2{Q}^2$