An infinitely long conducting cylindrical rod with a positive charge lambda per unit length is surrounded by a conducting cylindrical shell (which is also infinitely long) with a charge per unit length of -2 \lambda and radius r_1, as shown in the figure.
What is E(r), the radial component of the electric field between the rod and cylindrical shell as a function of the distance r from the axis of the cylindrical rod?
Express your answer in terms of lambda, r, and epsilon_0, the permittivity of free space.
The Attempt at a Solution
Basically I put a Gaussian surface just larger than the rod but smaller than the shell. First I calculate the electric field from the rod.
Thats field one. Now I do the same thing to calculate the second field
where q = -2[tex]\lambda[/tex]L
Now I should add the fields to find the field inside the shell and outside the rod and I get
That was my answer but im not sure if this is right or not