The differential area on the surface of a sphere in spherical coordinates is given on inside front cover of textbook, dS=dr sin(θ)dθ dφ. See sect. 1.4.1.
a. Verify that the surface area of a sphere of radius R is 4PiR^2.
b. Calculate the electric field (all components) at the center of a half-shell of
radius R. The surface of the half-shell is below the xy plane. It has uniform surface charge density, σ. The center of the sphere is also the origin of the coordinate system.
The Attempt at a Solution
I believe the given was supposed to be dS=r^2 sin(θ)dθ dφ. I did this part, assuming the problem was incorrect.
I integrated this as a double integral and got the correct result of 4PiR^2.
This is where I need help. I drew the diagram, and am having trouble getting it started. I know the general idea is to take a small section, and find E there, and integrate over the rest of the surface. I am having trouble carrying that idea out though. Any help is appreciated. Thanks in advance.