Question

What are the units of $K=\frac{1}{4\pi {\in }_0}$

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

Answer 1

Answer: (B)

By Coulomb's law
$F=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}$
$\therefore k=\frac{1}{4\pi {\epsilon }_0}=\frac{F{r}^2}{q^2}$ ( if $q_1=q_2=q$)
Hence, units of $k\frac{N{m}^2}{C^2}$
$=N{m}^2{C}^{-2}$