Prof. E. Carson’s lectures are quite clear, supplemental to Prof. Shankar’s Yale courses: https://www.youtube.com/watch?v=v57B_1ZBAho&list=PLZ6kagz8q0bvxaUKCe2RRvU_h7wtNNxxi .
What’s if it’s not a point charge in the center, but a sphere shell? This is when the superposition principle comes into play:
Placing a point charge in a place, and then place an atom to a distance to the point charge, there will be polarization.
From the point charge, we extend to calculate the field at a fixed location from an infinite rod and a ring.
Then filed of a finite disc
When the R goes to infinitive, it’s an infinite plane,
From this simple succinct equation, we know that the distance z doesn’t matter anymore, you always get the same field.