Question

Find the dimensions of electric permittivity.

• A. $[A^2{M}^{-1}{L}^{-3}{T}^4]$
• B. $[A^2{M}^{-1}{L}^{-3}{T}^0]$
• C. $[A{M}^{-1}{L}^{-3}{T}^4]$
• D. $[A^2{M}^0{L}^{-3}{T}^4]$

Answer 1

Answer: (A)

From Coulomb’s law, the force of attraction/repulsion between two point charges $q$, $q$ separated by distance $r$ is
$F=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r^2}$
$\Rightarrow {\epsilon }_0=\frac{1}{4\pi }\cdot \frac{q^2}{F{r}^2}$
where ${\epsilon }_0$ is electric permittivity.
Dimensions of ${\epsilon }_0=\frac{{\left[AT\right]}^2}{\left[ML{T}^{-2}\right]\left[L^2\right]}$
${\epsilon }_0=\left[A^2{M}^{-1}{L}^{-3}{T}^4\right]$