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## Homework Statement

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.

## Homework Equations

Gauss's law

## 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.

E(2L(pi)r)=Q/e

E=Q/(e(2L(pi)r))

Q=L[tex]\lambda[/tex]

E1=[tex]\lambda[/tex]/(e(2(pi)r))

Thats field one. Now I do the same thing to calculate the second field

E=q/(e(2L(pi)r))

where q = -2[tex]\lambda[/tex]L

E2= -2[tex]\lambda[/tex]/(e(2(pi)r))

Now I should add the fields to find the field inside the shell and outside the rod and I get

-[tex]\lambda[/tex]/(e(2(pi)r))

That was my answer but im not sure if this is right or not