Question

The constant of proportionality $\frac{1}{4\pi {\epsilon }_0}$ 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
$F=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}$
$\Rightarrow \left[\frac{1}{4\pi {\epsilon }_0}\right]=\frac{\left[F\times r^2\right]}{{\left[q\right]}^2}$
$=\frac{\text{[newton]}{\text{[}metre]}^2}{{\text{[coulmb]}}^2}$
$=N{m}^2{C}^{-2}$