What is the force on a point charge q1 contained inside a hollow conductive sphere (or fine grid) with charge q2 and radius R?
Coulomb F=k q1q2/r^2
Gauss Law/method of closed surface: Integral over closed surface of Enormal da = E times the area of the surface = Flux = must equal the enclosed charge / eps0.
The Attempt at a Solution
Am aware of familiar prediction that an _empty_ hollow sphere has no internal E field, which follows from applying gauss's law to any virtual surface internal to the sphere with no enclosed charge, therefore E must be zero everywhere. In this case w/ contained q1 there is some field. However, applying gauss's closed surface again seams to give just the solution for E from a point charge q: E=kq1/r^2 (r distance from q1) only, with no E contribution from the surrounding sphere. Thus no force on q1??? Ive done some computer sim. (2D only) by surrounding a pt charge w/ 2 dozen like pt charges arranged in a circle and then doing N - body Coulomb - there's plenty of resulting force on the internal charge excepting the center of the circle.
A little help please?