A) coulomb/newton-metre
B) newton - metre2/coulomb2
C) coulomb / newton ? metre
D) coulomb2/ (newton- metre)2
Correct Answer: C
Solution :
Key Idea: Substitute the units for all the quantities involved in an expression written for permittivity of free space. By Coulomb's law, the electrostatic force \[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\times \frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}\] \[\Rightarrow \]\[{{\varepsilon }_{0}}=\frac{1}{4\pi }\times \frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}F}\] Substituting the units for q, r and F, we obtain unit of \[{{\varepsilon }_{0}}=\frac{cons\tan t\times coulomb}{newton-{{(metre)}^{2}}}=\frac{{{(coulomb)}^{2}}}{newton-{{(metre)}^{2}}}\] \[={{C}^{2}}/N-{{m}^{2}}\]
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