1. A hollow insulating sphere with inner radius R and outer radius 2R carries a uniform volume charge density p. Positive charge q is distributed uniformly over the outer surface of the sphere. A point charge q is located at the center of the hollow space in the sphere. 2R Cl (a) Find the value of p so that the net charge of the entire system is zero. (b) lfp has the value you found in Part (a), find the electric field as a function of the distance r from the center in the regions 1' 2R. (c) In general, the electric field is only discontinuous at boundaries that carry a surface charge density. Explain how your results from Part (b) agree with this statement. 2. A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the xy-plane and given by the planes 2 = d and z = d. The x- and y-dimensions of the slab are infinite. The slab has a nonuniform volume charge density 22 9(2) = Po (E 1) where p0 is a positive constant. Use Gauss's law to find the electric field inside and outside the slab. (Hint: since the charge density is nonuniform, you'll have to use the general integral expression Qencl : f dQ = :0 dV encl encl to find the charge enclosed by the Gaussian surface. Think carefully about what expression you should use for the infinitesimal volume element dV.)