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Force Constant (k)

A proportionality constant in Coulomb's Law, representing the electrostatic field strength, dependent on the permittivity of free space.
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The statement of the theorem

Let q1q_1 and q2q_2 be two point charges located at positions r⃗1\vec{r}_1 and r⃗2\vec{r}_2 in a vacuum characterized by the permittivity ϵ0\epsilon_0. The electric field E⃗1\vec{E}_1 generated by q1q_1 at the position r⃗2\vec{r}_2 is given by the fundamental solution to Laplace's equation in electrostatics:\n\nE⃗1(r⃗2)=14πϵ0q1∣r⃗2−r⃗1∣2u^12\vec{E}_1(\vec{r}_2) = \frac{1}{4\pi\epsilon_0} \frac{q_1}{|\vec{r}_2 - \vec{r}_1|^2} \hat{u}_{12}\n\nwhere u^12=r⃗2−r⃗1∣r⃗2−r⃗1∣\hat{u}_{12} = \frac{\vec{r}_2 - \vec{r}_1}{|\vec{r}_2 - \vec{r}_1|} is the unit vector pointing from r⃗1\vec{r}_1 to r⃗2\vec{r}_2.\n\nThe electrostatic force F⃗21\vec{F}_{21} exerted on q2q_2 by q1q_1 is defined by F⃗21=q2E⃗1(r⃗2)\vec{F}_{21} = q_2 \vec{E}_1(\vec{r}_2). By comparing this definition with the standard form of Coulomb's Law, the Force Constant kk is rigorously defined as the proportionality factor relating the magnitude of the force to the product of the charges and the inverse square of the separation distance:\n\nF⃗21=kq1q2∣r⃗2−r⃗1∣2u^12\vec{F}_{21} = k \frac{q_1 q_2}{|\vec{r}_2 - \vec{r}_1|^2} \hat{u}_{12}\n\nEquating the two expressions yields the formal definition of kk:\n\nk=14πϵ0k = \frac{1}{4\pi\epsilon_0}
Source: Wikipedia