A) coulomb/newton-metre
B) \[newton-\text{ }metr{{e}^{2}}/coulom{{b}^{2}}\]
C) \[coulom{{b}^{2}}/\text{ }newton-metr{{e}^{2}}\]
D) \[coulom{{b}^{2}}/{{(newton-metre)}^{2}}\]
Correct Answer: C
Solution :
Key Idea: Substitute the units for all the quantities involved in an expression written for permittivity of free space. By Coulombs 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 \[{{\varepsilon }_{0}}=\frac{coulomb\times coulomb}{newton-{{(metre)}^{2}}}=\frac{{{(coulomb)}^{2}}}{newton-{{(metre)}^{2}}}\]
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