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