(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution

Part A:

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.

Part B:

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.

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# Homework Help: Electric Field at Center of Spherical Half-Shell

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