A) \[ML{{T}^{-1}}{{A}^{-1}}\]
B) \[ML{{T}^{-2}}{{A}^{-2}}\]
C) \[{{M}^{-1}}{{L}^{-3}}{{T}^{+4}}{{A}^{2}}\]
D) \[{{M}^{2}}{{L}^{-2}}{{T}^{-2}}{{A}^{2}}\]
Correct Answer: C
Solution :
Force, \[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}\]\[\Rightarrow \]\[{{\varepsilon }_{0}}=\frac{{{q}_{1}}.{{q}_{2}}}{4\pi F{{r}^{2}}}\] So dimension of \[{{\varepsilon }_{0}}\] \[=\frac{{{[AT]}^{2}}}{[ML{{T}^{-2}}][{{L}^{2}}]}=[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]\]You need to login to perform this action.
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