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 ?. Find the magnitude and direction of the electric field inside the hole, and show that is uniform over the entire hole. (?Hint:? See 22.57.) 22.57 . (a) An insulating sphere with radius a has a uniform charge density ?. 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 ?. 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).]

NEWTON: THE MIND THAT FOUND THE FUTURE ● different laws had to apply on earth and in the heavens ● science begins from theories or hypotheses that you have to prove ● in newton’s time, the gravity was in the apple ● all forces (including gravity) are between two objects, acting equally on both ○ newton’s 3rd law ● the natural path of a speeding object is a straight line, constant speed ○ uniform motion ● newton’s 1st law ● according to Halley, the force of gravity varies inversely with the square of the distance ● newton’s law of universal gravitation = everything attracts everything else ○ force is directly proportional to the two masses ○ force is inversely proportional to the separation of their ce