Question

What are the units of $K=\frac{1}{4\pi\,\in_0}$

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

Answer 1

Answer: (B)

By Coulomb's law
$F = \frac{ 1}{ 4 \pi \varepsilon_0 } \frac{ q_1 q_2 }{ r^2 } $
$\therefore k = \frac{ 1}{ 4 \pi \varepsilon_0 } = \frac{ Fr^2 }{ q^2 }$ ( if $q_1 = q_2 = q$)
Hence, units of $k \frac{ Nm^2 }{ C^2 } $
$= Nm^2 C^{ - 2} $