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Physics Question on coulombs law

The constant of proportionality 14πε0\frac{1}{4\pi\varepsilon_{0}} in Coulomb?s law has the following dimensions

A

C−2 N m2C^{-2}\,N\,m^{2}

B

C2 N−1 m−2C^{2}\,N^{-1}\,m^{-2}

C

C2 N m2C^{2}\,N\,m^{2}

D

C−2 N−1 m−2C^{-2}\,N^{-1}\,m^{-2}

Answer

C−2 N m2C^{-2}\,N\,m^{2}

Explanation

Solution

From Coulomb?s law
F=14πε0q1q2r2F=\frac{1}{4\pi\varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}}
⇒[14πε0]=[F×r2][q]2\Rightarrow \left[\frac{1}{4\pi\varepsilon_{0}}\right]=\frac{\left[F\times r^{2}\right]}{\left[q\right]^{2}}
=[newton][metre]2[coulmb]2=\frac{\text{[newton]} {\text[metre]}^{2}}{\text{[coulmb]}^{2}}
=Nm2C−2=Nm^{2}C^{-2}