A very long, solid insulating cylinder with radius $R$ has a cylindrical hole with radius $a$ bored along its entire length. The axis of the hole is a distance $b$ from the axis of the cylinder, where $a < $
$b < R$ (Fig. P22.62). The solid material of the cylinder has a uniform volume charge density $\rho .$ Find the magnitude and direction of the electric field $\vec{\boldsymbol{E}}$ inside the hole, and show that $\vec{\boldsymbol{E}}$ is uniform over the entire hole. (Hint: See Problem $22.61 . )$