Chapter 24, Problem 9P

You are working on a laboratory device that includes a small sphere with a large electric charge Q. Because of this charged sphere, there is a strong electric field surrounding your device. Other researchers in your laboratory are complaining that your electric field is affecting their equipment. You think about how you can obtain the large electric field that you need close to the sphere but prohibit the field from reaching your colleagues. You decide to surround your device with a spherical transparent plastic shell of radius R. The plastic has a very thin coating of conducting material on the outside that only minimally reduces the transparency of the material. The shell is placed so that the small sphere is at the exact center of the shell. Determine to what electric potential the outer shell must be raised to completely eliminate the electric field outside of the shell.