I started reading through "Electricity and Magnetism" by Purcell and came across the derivations for infinite line and infinite plane charge distributions and noticed the former has a 1/r dependency (on perpendicular distance from the wire) and a constant value for the plane.(adsbygoogle = window.adsbygoogle || []).push({});

Would an infinite charge volume have a linear dependency on r, eg constant*r?

I don't have the multivariable calculus knowledge to work this through myself to see, but this is just out of interest right now ...

I've thus far reasoned that this might be so by considering that E=0 at the center of the distribution (from symmetry) and then moving a distance r out from the center would produce a cuboid of charge, an infinite plane face and thickness r and thus the flux would be like taking the single variable integral of a bunch of infinite plane electric fields (which I assume have a constant electric field strength as in the book) from 0->r ... thus introducing a linear r dependency?

Is this ad hoc reasoning ok or am I way off?

I expect to cover the calculus sometime in the next few weeks anyway so I can hopefully form the equations up myself ... but this is bugging me since I thought about it first :(

**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!

# Homework Help: Electric field at a point within an infinite volume charge distribution

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