Question

Find the dimensions of electric permittivity.

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

Answer 1

Answer: (A)

$[A^2M^{-1}L^{-3}T^4]$

Answer 2

From Coulomb?? law, the force of attraction/repulsion between two point charges $q$, $q$ separated by distance $r$ is
$F = \frac{1}{4\,\pi\,\varepsilon_{0}} \frac{q^{2}}{r^{2}}$
$\Rightarrow \varepsilon _{0} = \frac{1}{4\,\pi } \cdot \frac{q^{2}}{Fr^{2}}$
where $e_{0}$ is electric permittivity.
Dimensions of $\varepsilon_{0} =\frac{\left[AT\right]^{2}}{\left[MLT^{-2}\right]\left[L^{2}\right]}$
$\varepsilon_{0} = \left[A^{2}\,M^{-1}\,L^{-3}\,T^{4}\right]$