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## Homework Statement

Charge is distributed through an infinitely long cylinder of radius R in such a way that the charge density is proportional to the distance from the central axis: ß = A r, where A is a constant and ß is the density.

(a) Calculate the total charge contained in a segment of the cylinder of length L.

(b) Calculate the electric field for points outside the cylinder.

(c) Calculate the electric field for points inside the cylinder.

## Homework Equations

Gauss' Law

## The Attempt at a Solution

so for a)

dQ = p(r) V dr

right? or is it

dQ = p(r) A dr

I can't decide. It says charge is distributed throughout the cylinder but in my book we always seem to use surface areas so I'm confused.

But if I go with my first equation and integrate to find the total charge, Q

Q = integral (A * r * pi * R

^{2}* L * dr)

where r = distance of point from central axis and R = radius of cylinder

then = A * pi * R

^{2}* L * integral r dr

which = (A * pi * R

^{4}* L)/2

I integrated from 0 to R which leaves out half of the cylinder so I'm not so sure what to do about that... should I integrate to 2R intsead?

As far as for b and c, I can't see why they'd be different. My book talks about cylindrical symmetry and says

E = linear charge density/(2 * pi *e

_{0}* r)

which is the electric field E due to an infinitely long, straight line of charge, at a point that is a radial distance r from the line. So wouldn't they be the same, with different r's? Perhaps for the one inside the surface, the density B = A * r would cancel with the r on the bottom. Or instead of this equation, should I go back and say:

e

_{0}* E * A = q

and use my q from before, if it's even right?

And should I use the area or the volume then, for this part?

Ugh this electric stuff confuses me. I miss gravity...