1) If the electric ﬁeld in some region is given (in spherical coordinates) by the expression
E(r) = (A* r(hat)+ B sin θ cos φ* φ(hat)) /r ,
where A and B are constants,
what is the charge density?
2) A metal sphere of radius R, carrying charge q, is surrounded by a thick concentric metal shell (inner radius a, outer radius b). The shell carries no net charge.
(a) Find the surface charge density σ at R, at a, and at b.
(b) Find the potential at the center, using inﬁnity as the reference point.
(c) Now the outer surface is touched to a grounding wire, which lowers its potential
to zero (same as inﬁnity). How do your answers to (a) and (b) change?
3) What is the force of attraction between q and a grounded conducting sphere?
This in-depth solution shows step-by-step calculations and annotated diagrams to determine the charge density of the electric field, surface charge density, potential at the center of the sphere, charge with a grounding wire and also the force of attraction.