A conducting spherical shell with inner radius ‘a’ and outer radius ‘b’ has a positive charge Q located at its center. The total charge on the shell is -4Q, and it is insulated from its surroundings. (a) Derive expressions for the electric field magnitude in terms of the distance ‘r’ from the center for the regions: r , a; a < r < b; r >b.

(b) What is the surface charge density on the inner surface of the conducting shell?

(c) What is the surface charge density on the outer surface of the conducting shell?

(d) Draw a sketch showing electric field lines and the location of all charges.

(e) Draw a sketch of the electric field E as a function of