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## Homework Statement

There are 2 long coaxial insulating cylinder. The inner and outer cylinders have radii of a and b and charge densities λ and -λ uniformly distributed on the surface. Calulcate energy per unit length 2 ways (equations below)

## Homework Equations

W = [itex]\frac{1}{2}[/itex][itex]\int σ V da[/itex]

W = [itex]\frac{ε0}{2}[/itex][itex]\int E^2 dτ[/itex]

## The Attempt at a Solution

So using gausses law, with s (radius of cyliunder) < a there is no electric field as there is no enclosed charge. Outside both cylinders there is no E because there is no net charge. SO the only E and energy is between the 2 cylinders.

So I have to do it 2 ways, one with the first and one with the second. I am unsure though how to set up gauss's law to find the E field. Also since we are using line charge how does that change things?

So i wrote |E|* 2*pi*l*s =1/ε0[itex]\int λ*2*pi*s*dl[/itex]

but this doesn't seem right. I am unsure how to deal with the line charge. Do i use like surface charge still but write it as σ = 2*pi*r*dl but what are the limits of integration? I am just a little confused at this part. Help would be nice! Thanks