Question

Is the value of $k=\frac{1}{4\pi ϵ}$ experimentally found? Or is it derived? If it is derived, how?

Answer 1

Yes, it was experimentally performed by the scientist. The proportionality constant $\frac{1}{4\pi {ϵ}_0}$, called the Coulomb constant (k) (sometimes called the Coulomb force constant), is related to defined properties of space.
$k=\frac{1}{4\pi {ϵ}_0}$
${ϵ}_0=8.85\times {10}^{-12}{C}^2/N-m^2$ (${ϵ}_0$ is the "permittivity of free space")