What are the units of K=(\frac{1}{4\pi,\in\_0}) | Physics | SolveeIt

Question

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

$C^2 \, N^{ - 1} \, m^{ - 2}$

$Nm^2 C^{ - 2 }$

$Nm^2 C^2$

Unitless

Answer

$Nm^2 C^{ - 2 }$

Explanation

Solution

By Coulomb's law F = $\frac{ 1}{ 4 \pi \varepsilon_0 } \frac{ q_1 q_2 }{ r^2 }$ $\therefore k = \frac{ 1}{ 4 \pi \varepsilon_0 } = \frac{ Fr^2 }{ q^2 }$ $\hspace20mm$ $( if \, q_1 = q_2 = q )$ Hence, units of k $\frac{ Nm^2 }{ C^2 }$ = $Nm^2 C^{ - 2}$

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