Sphere and cones **

(a) Consider a fixed hollow spherical shell with radius R and sur- face charge density σ . A particle with mass m and charge -q that is initially at rest falls in from infinity. What is its speed when it reaches the center of the shell? (Assume that a tiny hole has been cut in the shell, to let the charge through.)

(b) Consider two fixed hollow conical shells (that is, ice cream cones without the ice cream) with base radius R, slant height L, and surface charge density σ , arranged as shown in Fig. 1.46. A particle with mass m and charge -q that is initially at rest falls in from infinity, along the perpendicular bisector line, as shown. What is its speed when it reaches the tip of the cones?

You should find that your answer relates very nicely to your answer for part (a).