I recently had a problem set with two questions that seemed to give very similar answers. I'm not asking how to do this, so I don't think this post belongs in the homework section. Rather, I'm asking if the similarity I think I see has any deeper meaning in the physics of electric fields.(adsbygoogle = window.adsbygoogle || []).push({});

Let's say I want to find the electric field due to a disk of uniform charge density along the disk's axis. I would integrate and I end up getting something like:

E=∫(2*pi*sigma*z*r*dr)/(r^2+z^2)^3/2... note that z/sqrt(r^2+z^2) comes in from multiplying by the cosine of the angle to get only the portion along the axis. In this integral, z is a constant.

For a hollow cylinder, you get essentially the same integral: E=∫(2*pi*sigma*R*z*dz)/(R^2+z^2)^(3/2)... again, note that R/sqrt(R^2+z^2) come from the cosine of the angle for similar reasons. In this case, R is a constant.

So they seem to be the same integral with R and z swapped out. Other than the fact that sigma is different in each case, does the similarity mean anything? It's almost like it's saying that a cylinder and a circle have basically the same electric field along the axis.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Circular vs. Cylindrical Charge Distribution

**Physics Forums | Science Articles, Homework Help, Discussion**