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1) A positive charge distribution exists within a volume of an infinitely long cylindrical shell of inside radius [tex]a[/tex] and outside radius [tex]b[/tex]. The charge density [tex]\rho[/tex], is not uniform but varies inversely as the radius [tex]r[/tex] from the axis. That is, [tex]\rho=\frac{k}{r}[/tex] for [tex]a<r<b[/tex] where [tex]k[/tex] is a constant. (a) Find the total charge Q in a length L of the cylindrical shell and (b) starting with Gauss' Law, find the electric field at a point [tex]r[/tex] within the cylinder, [tex]a<r<b[/tex].Answera) [tex]Q=k 2 \pi L(b-a)[/tex] b) [tex]E=\frac{k (r-a)}{ \varepsilon_0 r}[/tex]

2) The axis of a long hollow metallic cylinder (inner radius 1 cm and outer radius 2 cm) is coaxial with a long wire. The wire has a linear charge density of -8 pC/m and the cylinder has a net charge per unit length of -4 pC/m. Derive an expression for the electric field outside the cylinder and determine the magnitude of the electric field at a point 3 cm from the axis.Answer7.2 N/C

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