Sphere in a cylinder **
An infinite cylinder with uniform volume charge density ρ has its axis lying along the z axis. A sphere is carved out of the cylin- der and then filled up with a material with uniform density -ρ/2. Assume that the center of the sphere is located on the x axis at position x = a. Show that inside the sphere the component of the field in the xy plane is uniform, and find its value. Hint: The technique used in Problem 1.27 will be helpful.