A) \[{{A}^{2}}{{T}^{2}}{{M}^{-1}}{{L}^{-3}}\]
B) \[{{A}^{2}}{{T}^{4}}{{M}^{-1}}{{L}^{-3}}\]
C) \[{{A}^{-2}}{{T}^{-4}}M{{L}^{3}}\]
D) \[{{A}^{2}}{{T}^{-4}}{{M}^{-1}}{{L}^{-3}}\]
Correct Answer: B
Solution :
\[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\,\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}\] \[\Rightarrow \] \[{{\varepsilon }_{0}}=\frac{|{{q}_{1}}|\,|{{q}_{2}}|}{[F]\,[{{r}^{2}}]}=\frac{[{{A}^{2}}{{T}^{2}}]}{[ML{{T}^{-2}}]\,[{{L}^{2}}]}=[{{A}^{2}}{{T}^{4}}{{M}^{-1}}{{L}^{-3}}]\]
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