Calculating electric fields through integration

[EpiGen]

Can anyone find a website that shows you how to calculate the electric field by integration for a evenly distributed disk and a hollow ring? I tried figuring it out myself but all the websites I found skipped many steps on the math. Thanks!

 

[stevenb]

Can anyone find a website that shows you how to calculate the electric field by integration for a evenly distributed disk and a hollow ring? I tried figuring it out myself but all the websites I found skipped many steps on the math. Thanks!

Are you looking for the "on-axis" solution, or a solution for any point in space?

 

[EpiGen]

Oh sorry on axis. Anything that would help me understand it would be greatly appreciated!

 

[stevenb]

Oh sorry on axis. Anything that would help me understand it would be greatly appreciated!

Well there are many links, for example.

http://planetphysics.org/encyclopedia/ElectricFieldOfAChargedDisk.html

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html

http://www.phys.uri.edu/~gerhard/PHY204/tsl36.pdf

I'm guessing you've searched and seen these or similar links. I suppose these do skip some steps, but if you look at different links, you may be able to piece the whole thing together.

If not, perhaps you can clarify which parts of these derivations are not detailed enough.

I don't know if this will be useful, but I can provide my derivation of the disc solution that takes a slightly different approach by calculating the answer for a disk of finite thickness (rather than infinitely thin as is usually done). After doing this, I take the limit as the thickness goes to zero to get to the usual answer. I once worked out this derivation for a different question (related to the charged disk) that came up in another forum. I figure I should post it in case one of your points of confusion is the concept of an infinitely thin disk, which is somewhat unrealistic. However, if this is not your point of confusion and if this creates any confusion whatsoever, then just ignore it and focus on the textbook approach.