I'm stuck on two problems. I hope someone can help me. Here they are...

1) For 1a I thought Q would be [tex]Q=\rho \pi L (b^2-a^2)[/tex] but since [tex]\rho=\frac{k}{r}[/tex] so [tex]Q=\frac {k \pi L (b^2-a^2)}{r}[/tex]. After being stumped on 1a I'm not sure how to go about 1b.

2) I've derived about 4 equations for this problem (all wrong of course) and I get numbers like 4.7 N/C or so but never 7.2 N/C. I think the wire inside the cylinder is really screwing me up.

I'd really appreciate some help. Even a little nudge in the right direction would be great. Thank you thank you thank you

Hey thanks for the reply; could you give me a quick explanation on how you got that answer? Just understanding the process you went through would really help me a lot. Thanks.

You need to start with definitions, in a question such as this one;

[tex] Q = \int_{V} \rho d\tau [/tex]

is a good place to start. Instead of performing a triple integral, utilize the symmetry of the cylinder to express dV in terms of dr, thus reducing it to a single integral.

Ok I'm pretty sure I understand the first problem now.

Like Krab said for 1a) [tex]Q=\int^b_a \frac{k}{r} 2 \pi r L dr = k 2 \pi L \int^b_a dr = k2\pi L (b-a)[/tex]
Since the total charge is asked for you must integrate from a to b.

To find the charge for 1b) you have to integrate from a to r so [tex] q=k2 \pi L(r-a)[/tex] and [tex]E=\frac{k2 \pi L(r-a)}{\varepsilon_0 2 \pi L r}[/tex] which is simply [tex]E=\frac{k(r-a)}{\varepsilon_0 r}[/tex]

Thanks for the help. I'm still stuck on deriving an expression for #2 though. I'd really appreciate even just a hint to get me started. Thanks again!

Ok, I've been working on this problem for an insane amount of time but I never get 7.2 N/C. Can someone check the expression I came up with and tell me if it's right? This is for the second question...

[tex] \lambda L + \rho \pi L(b^2-a^2) = \varepsilon_0 E 2 \pi r L[/tex]

where lambda is the charge density of the wire, rho is the charge density of the cylinder, b is the outside radius, a is the inside radius, and r is the distance from the axis (r is greater than b).

If I plug in the numbers from the problem I do not get the answer quoted. What am I doing wrong here?

Your expression is no good. It also looks much more complicated than it needs to be. Hint: Since you only care about the field outside the cylinder, the net linear charge density is just the sum of that for the wire and the cylinder.