Calculating E in a hemispherical shell using Coulomb's law

[Lisa...]

My teacher worked out the following problem as shown below:

http://img116.imageshack.us/img116/7656/naamloos27mf.gif

The only thing is I don't really understand what he's doing, so could anybody please explain to me a bit more which steps he takes? I would be very greatful! (or maybe there's an easier way to solve it...)

 

[dicerandom]

Basically what he's doing is slicing the hemisphere into a whole bunch of tiny rings. Presumably equation 23-10 describes the electric field generated by a ring along the axis which runs through its center. Due to symmetry in x and y (there's just as much charge to one side of the ring as the other) the electric field along this axis must be entirely in z.

The rest of it is just some geometry on the surface of the sphere, unfortunately I don't have time to draw a picture and scan it just now. If nobody else has replied by the time I get back from class I'll see if I can whip something up for you.

 

[dicerandom]

Hi Lisa,

I wrote up the problem and scanned it, hopefully this will help. I derived the E field from a ring of charge up near the top since I didn't have a handy reference. I then drew out the geometry on the surface of the sphere and used that to relate back to the field from the ring of charge. Hopefully this will help you see what's going on.

The file is http://www.warpenguin.com/~dice/hemisphere.jpg , it's huge though. I think you should be able to print it out and it should look okay, or you can just zoom out and read it on your monitor.

Let me know if you have any questions