Solution
= Solution
Writing $r=|x|$ and imposing continuity gives
$$
\phi(r)=\frac{\rho_0}{2\varepsilon_0}\begin{cases}2(b-a),&r\lt a,\\2b-r-a^2/r,&a\le r\le b,\\(b^2-a^2)/r,&r\gt b.\end{cases}
$$
= Solution
Writing $r=|x|$ and imposing continuity gives
$$
\phi(r)=\frac{\rho_0}{2\varepsilon_0}\begin{cases}2(b-a),&r\lt a,\\2b-r-a^2/r,&a\le r\le b,\\(b^2-a^2)/r,&r\gt b.\end{cases}
$$