Answer:
Solution for 3 different cases are given in explanation.
Explanation:
Gauss's Law:
[tex]\int_S E.dA=Q_{encl}/\epsilon_0[/tex]
for [tex]r<r_0[/tex] :
[tex]E.2\pi rL=\frac{\rho\pi r^2L/\pi r_0^2}{\epsilon_0} \\\\E=\frac{\rho r}{2\pi\epsilon_0 r_0^2}[/tex]
for [tex]r=r_0[/tex] :
[tex]E.2\pi r_0L=\frac{\rho\pi r_0^2L}{\epsilon_0} \\\\E=\frac{\rho r_0}{2\epsilon_0}[/tex]
for [tex]r>r_0[/tex] :
[tex]E.2\pi rL=\frac{\rho\pi r_0^2L}{\epsilon_0} \\\\E=\frac{\rho r_0^2}{2\epsilon_0 r}[/tex]
