Answer to Question #92825 in Electricity and Magnetism for Kyle

Question

Assume theres a charge at point P outside a sphere of charge. How do we calculate the electric field at point P by treating the sphere of charge as a collection of thin disks of charge and without using Gauss's Law?

Answer 1

We draw the axis through the center of the sphere and point P, then divide the surface of the sphere into infinitely thin rings whose plane is perpendicular to the axis, and the radius is determined by the distance from the center of the sphere, using the principle of superposition we find the field strength at point P created by each such ring, and then, again using the principle of superposition, we calculate, by integrating from minus to plus the radius of the sphere, the resulting field from all such rings.

The way is a little laborious, but knowledge of the Gauss theorem is not required!