Q. Dimensions of $\varepsilon_{0}$ are
A) $M^{- 1}L^{- 3}T^{4}A^{2}$
B) $M^{0}L^{- 3}T^{3}A^{3}$
C) $M^{- 1}L^{- 3}T^{3}A^{\ }$
D) $M^{- 1}L^{- 3}T^{\ }A^{2}$
Explanation
(a) From $F = \frac{1}{4\pi\varepsilon_{0}\ }\begin{array}{r}
\ \\
\
\end{array}\frac{q_{1}q_{2}}{r^{2}}$
$\varepsilon_{0} = \frac{1}{4\pi F\ }\begin{array}{r}
\ \\
\
\end{array}\frac{q_{1}q_{2}}{r^{2}} = \frac{\left\lbrack A^{2}T^{2} \right\rbrack}{\left\lbrack MLT^{- 2} \right\rbrack\left\lbrack L^{2} \right\rbrack}$
$= \lbrack M^{- 1}L^{- 3}T^{4}A^{2}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.