Question

What are the units of $K=1/4\pi {\epsilon }_0?$

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

Answer 1

Answer: (B)

From Coulomb's law two stationary point charges $q_1$ and $q_2$ attract or repel each other with a force $F$ which is directly proportional to the product of the charges and inversely proportional to the square of distance between them,
i.e., $F=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}$
$\therefore K=\frac{1}{4\pi {\epsilon }_0}=\frac{F{r}^2}{q^2}$ (if $q_1=q_2=q)$
Hence, units of $K=\frac{N{m}^2}{C^2}$
$=N{m}^2{C}^{-2}$