It is possible that we do not have to account for 3D space using the factor √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, ne is,
ne=n2=772
half the total number of particles in a charge, n.
So,
qadj=19.029022e26∗2ln(cosh(3.135009))4π×10−7∗772=1.658431e−19
in any one direction.
Good night...
If we really fuss about it,
⌈772⌉=⌈38.5⌉=38
when the experiment to find the elementary charge e is using repulsive force and the situation is presented with the least repulsive force.
qadj=19.029022e26∗2ln(cosh(3.135009))4π×10−7∗⌈772⌉=1.636893e−19
Good morning!