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) \[[{{A}^{2}}{{M}^{0}}{{L}^{-3}}{{T}^{4}}]\]
Correct Answer: A
Solution :
From Coulombs law, The force of attraction or repulsion between two point charges q, q separated by distance r is \[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}^{2}}}{{{r}^{2}}}\] \[\Rightarrow \] \[{{\varepsilon }_{0}}=\frac{1}{4\pi }\frac{{{q}^{2}}}{F{{r}^{2}}}\] where \[{{\varepsilon }_{0}}\] is electric permittivity. Dimensions of \[{{\varepsilon }_{0}}=\frac{{{[AT]}^{2}}}{[ML{{T}^{-2}}]\,[{{L}^{2}}]}\]
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