Fundamental Physics/Force/Electrostatic Force

The attraction force of negative charge attracts the positive charge calculated by Coulom's law

${\displaystyle F={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}\,r^{2}}}=K{\frac {q_{1}q_{2}}{r^{2}}}}$


Where:

${\displaystyle F\ }$ is the magnitude of the force exerted,
${\displaystyle q_{1}\ }$ is the charge on one body,
${\displaystyle q_{2}\ }$ is the charge on the other body,
${\displaystyle r\ }$ is the distance between them,
${\displaystyle \varepsilon _{0}\ }$ is the electric constant or permittivity of free space or permittivity of the vacuum. It is 8.854×10−12 C2 N-1 m-2 (also F m-1)

${\displaystyle K={\frac {1}{4\pi \varepsilon _{0}\,}}}$

The occurrence of ${\displaystyle 4\pi }$ with the constant is related to some geometrical considerations that make some formulas (notably Maxwell's Equations) simpler. Ultimately it has to do with the fact that the surface area of a sphere is ${\displaystyle 4\pi }$. Much ink has been spilled over this issue—one sometimes sees equations in "rationalized SI units" instead of the "plain" SI units that we use here.

In Vector Form, the force is in the direction of making like charges repel and unlike charges attract. It could be written in vector form as:

${\displaystyle {\vec {F}}_{2,1}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}\,r^{2}}}{\hat {r}}_{2,1}}$

Where:

${\displaystyle F_{2,1}}$ is the force vector acting on charge 2, coming from charge 1
${\displaystyle {\hat {r}}_{2,1}}$ is the unit vector from particle 1 to particle 2, that is, the actual spatial vector divided by its length. Its length is of course ${\displaystyle r}$. The formula could be written as:
${\displaystyle {\vec {F}}_{2,1}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}\,r^{3}}}{\vec {r}}_{2,1}}$
It is sometimes useful, in investigations of optics and capacitor dielectrics, to use a value of ε other than the standard "vacuum" value, since doing so can automatically handle the behavior of the dielectric. When this is done, it is common to use the symbol ${\displaystyle \varepsilon _{0}}$ ("epsilon-nought") to denote the vacuum value, and ${\displaystyle \varepsilon }$ to denote the modified value. When this is done, the more common formula is:
${\displaystyle F={\frac {q_{1}q_{2}}{4\pi \varepsilon \,r^{2}}}}$