Question

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

• A. $ C^{-2}\,N\,m^{2} $
• B. $ C^{2}\,N^{-1}\,m^{-2} $
• C. $ C^{2}\,N\,m^{2} $
• D. $ C^{-2}\,N^{-1}\,m^{-2} $

Answer 1

Answer: (A)

From Coulomb’s law
$F=\frac{1}{4\pi\varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}} $
$\Rightarrow \left[\frac{1}{4\pi\varepsilon_{0}}\right]=\frac{\left[F\times r^{2}\right]}{\left[q\right]^{2}}$
$=\frac{\text{[newton]} {\text[metre]}^{2}}{\text{[coulmb]}^{2}}$
$=Nm^{2}C^{-2}$