Consider a grounded, conducting, spherical shell of outer radius b and inner radius a. Using the method of images, dicuss the problem of a point charge q inside the shell, i.e. at a distance r<a from the center. Find a) the potential inside the sphere; b) the induced surface charge density on the inner surface of the shell at r=a; what is the total induced charge? c) the magnitude and direction of the force acting on q. Does q get pushed towards the center, or away from the center? d) Is there any change in the solution if the sphere is kept at a fixed potential φo? If the sphere has a fixed total charge Q?

Consider a grounded, conducting, spherical shell of outer radius b and inner radius a. Using the method of images, dicuss the problem of a point charge q inside the shell, i.e. at a distance r<a from the center. Find a) the potential inside the sphere; b) the induced surface charge density on the inner surface of the shell at r=a; what is the total induced charge? c) the magnitude and direction of the force acting on q. Does q get pushed towards the center, or away from the center? d) Is there any change in the solution if the sphere is kept at a fixed potential φo? If the sphere has a fixed total charge Q?