How did it get to that? Stretching Coulomb's law...
1. The problem statement, all variables and given/known data
The charge is distributed with uniform
surface density σ on the disk of radius R. Find the potential
at the axis of the disk.
2. Relevant equations
Coulomb's law and the definition of a electric potential at point x
3. The attempt at a solution
I have a solution in front of me but can't understand some step inside it:
The potential can be defined now
phi(x)= (1/4pi*epsilon0)Integral[(sigma(x')/|x-x'|)dS'] and the solution for the integral from 0 to R is:
Now, the electric field at this point is:
I can clearly follow until now, but then the book says that for z>>R we get
where Q is the total charge of the disc.
How can it be proportional to 1/z?? when I take z>>R - I get E(z)=0...