Electrostatic Constant Written Funny

The ε₀ is a constant called the electric permittivity of free space. Read about it here: http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/elefie.html#c3"

 

It's partly for historical reasons, and partly a matter of minimizing the number of equations that have factors of [itex]4 \pi[/itex].

Using [itex]\epsilon_0[/itex] Coulomb's Law is more complicated:

[tex]F_{elec} = \frac {1} {4 \pi \epsilon_0} \frac {q_1 q_2} {r^2}[/tex]

but other equations like Gauss's Law and the parallel-plate capacitor equation are simple:

[tex]\vec \nabla \cdot \vec E = \frac {\rho} {\epsilon_0}[/tex]

[tex]C = \frac {\epsilon_0 A}{d}[/tex]

Whereas using k, Coulomb's Law is simpler:

[tex]F_{elec} = k \frac {q_1 q_2} {r^2}[/tex]

but you have to insert factors of [itex]4 \pi[/itex] into other equations:

[tex]\vec \nabla \cdot \vec E = 4 \pi k \rho[/tex]

[tex]C = \frac {A}{4 \pi k d}[/tex]