It is possible that we do not have to account for 3D space using the factor \(\sqrt{3}\), but must account for the fact that the single charge is a lump of \(77\) particles. In any one direction half of these particles on one side shield the other half of the particles on the other side. In effect, a test charge only faces half of the total number of particles in a single charge. The effective number of particles, \(n_e\) is,
\(n_e=\cfrac{n}{2}=\cfrac{77}{2}\)
half the total number of particles in a charge, \(n\).
So,
\(q_{adj}=\cfrac{1}{9.029022e26}*\cfrac{2ln(cosh(3.135009))}{4\pi\times10^{-7}}*\cfrac{77}{2}=1.658431e−19 \)
in any one direction.
Good night...
If we really fuss about it,
\(\left\lceil\cfrac{77}{2}\right\rceil=\left\lceil38.5\right\rceil=38\)
when the experiment to find the elementary charge \(e\) is using repulsive force and the situation is presented with the least repulsive force.
\(q_{adj}=\cfrac{1}{9.029022e26}*\cfrac{2ln(cosh(3.135009))}{4\pi\times10^{-7}}*\left\lceil\cfrac{77}{2}\right\rceil=1.636893e-19 \)
Good morning!
