# Gauss law 2

by hover
Tags: gauss
 P: 344 1. The problem statement, all variables and given/known data 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. 2. Relevant equations Gauss's law 3. 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$$\lambda$$ E1=$$\lambda$$/(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$$\lambda$$L E2= -2$$\lambda$$/(e(2(pi)r)) Now I should add the fields to find the field inside the shell and outside the rod and I get -$$\lambda$$/(e(2(pi)r)) That was my answer but im not sure if this is right or not