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

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.

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 :(

unless you're considering the electric field in the 4-th dimension, the electric field for an infinite volume distribution has to be 0. An infinite charge volume would stretch out over the entire universe and the test charge would have to be inside the conducting material unless it was outside the universe (huh??) or in a higher dimension (huh??)

No need to be flippant about it, I find that considering and trying to extend/generalise everything I come across even it if seems or is unphysical to be useful mental exercise.

So, my question becomes:

If there were 4 or more spatial dimensions, then would the above hold true?

sorry if i came off as flippant, i was actually trying to be humorous (evidently, that failed)

im a student barely ahead of you so i have no clue about its behavior in 4d

Ah, ok ... I read overtones on the (huh???) that were incorrect, sorry about that. Anyway, there are bigger fish to fry at this time of year so I'll consider this effectively closed.