k = 9 000 000 000
Formula
Magnitude of the force with which two point charges in vacuum act on each other
ENT-level problem
Two point charges $q_1 = 2$ uC and $q_2 = 3$ uC are placed $r = 0.1$ m apart. Find the electrostatic force between the charges. Coulomb's constant is $k = 9 \cdot 10^9$ N·m²/C².
Coulomb's law:
$$F = k \frac{q_1 q_2}{r^2} = 9 \cdot 10^9 \cdot \frac{2 \cdot 10^{-6} \cdot 3 \cdot 10^{-6}}{(0.1)^2}$$
$$F = 9 \cdot 10^9 \cdot \frac{6 \cdot 10^{-12}}{10^{-2}} = \frac{54 \cdot 10^{-3}}{10^{-2}} = 5.4 \text{ N}$$
In vacuum k = 9 · 10⁹ N·m²/C²; in air the value is nearly the same.
The force falls off with the square of the distance: twice as far — four times weaker (inverse square, like gravity).
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