Problem #3: Gauss' Law: Electric Field Calculation (Cylindrical Symmetrles).
A positive line charge with line charge density +\lambda is at the center of a thick conducting cylindrical shell that has line
charge density -\lambda/3. The conducting cylindrical shell has inner radius $r_1$ and outer radius $r_2$.
Consider three points of interest A, B, and C, at radii from the center $r_A$, $r_B$, and $r_C$.
As shown in the figure, $0 < r_A < r_1$, $r_1 < r_B < r_2$, and $r_C > r_2$.
5. Determine $\lambda_1$ and $\lambda_2$, the induced surface charge densities on the inner and outer surfaces of the conducting
shell, respectively.
6. Assuming that $\lambda = +2$ C/m, $r_1 = 0.15$ m, and $r_2 = 0.20$ m, calculate the electric field at position C, a distance
$r_C = 0.25$ m from the center.
