A very long, solid insulating cylinder has radius R; bored along its entire length is a...

A very long, solid insulating cylinder has radius R; bored along its entire length is a cylindrical hole with radius a. The axis of the hole is a distance b from the axis of the cylinder, where a < b < R (Fig. P22.58). The solid material of the cylinder has a uniform volume charge density ρ. Find the magnitude and direction of the electric field inside the hole, and show that is uniform over the entire hole. (Hint: See Problem 22.57.)

22.57 . (a) An insulating sphere with radius a has a uniform charge density ρ. The sphere is not centered at the origin but at Show that the electric field inside the sphere is given by (b) An insulating sphere of radius R has a spherical hole of radius a located within its volume and centered a distance b from the center of the sphere, where a < b < R (a cross section of the sphere is shown in Fig. P22.57). The solid part of the sphere has a uniform volume charge density ρ. Find the magnitude and direction of the electric field inside the hole, and show that is uniform over the entire hole. [Hint: Use the principle of superposition and the result of part (a).]