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## Homework Statement

two very long coaxial cylinders. Inner has radius a and is solid with charge per unit length of λ. Volume is also uniform but not defined by a parameter. Outer is hollow with inner radius b and outer radius c. Outer cylinder is a conductor with charge per unit length of -2λ. Find E(r) for all r in terms of given parameters. you can also view attached picture.

## Homework Equations

∫E.dA=q

_{enclosed}/ε

_{0}

## The Attempt at a Solution

I'm hung up right away on what to do with the inner radius from 0->a Ive got the left side of the equation I think, but I don't know how to get q

_{enclosed}in terms of r, if it needs to be. I expect to integrate on that part. Anywho here's where I'm at.

E2∏rh=(1/ε

_{0})∫dq

I've got λ=dq/dh where h represents the length of the cable being considered. All the examples seem to use charge density rather than charge per unit length, using this gives me:

E2∏rh=(1/ε

_{0})∫λdh which is not in terms of r. I suppose I could still integrate it and cancel h on both sides, let me know if that's wrong.

E2∏rh=(λh/ε

_{0})→E2∏r=(λ/ε

_{0})

E(r)=λ/(2∏r*ε

_{0})

Is this wrong for any reason? It doesn't feel right to not use the radius on the right side.