1996E1. A solid metal sphere of radius a is charged to a potential Vo>0 and then isolated from the charging source. It is then surrounded by joining two uncharged metal hemispherical shells of inner radius b and outer radius 2b, as shown above, without touching the inner sphere or any source of charge.
a. In terms of the given quantities and fundamental constants, determine the initial charge Qo on the solid sphere before it was surrounded by the outer shell.
b. Indicate the induced charge on the following after the outer shell is in place.
i. The inner surface of the shell
ii. The outer surface of the shell
c. Indicate the magnitude of the electric field as a function of r and the direction (if any) of the field for the regions indicated below. Write your answers on the appropriate lines.
i. r<a Magnitude \\_\\_\\_ Direction \\_\\_\\_
ii. a<r<b Magnitude \\_\\_\\_ Direction \\_\\_\\_
iii. b<r<2b Magnitude \\_\\_\\_ Direction \\_\\_\\_
iv. 2b<r Magnitude \\_\\_\\_ Direction \\_\\_\\_
d. Does the inner sphere exert a force on the uncharged hemispheres while the shell is being assembled? Why or why not?
e. Although the charge on the inner solid sphere has not changed, its potential has. In terms of Vo, a, and b, determine the new potential on the inner sphere. Be sure to show your work.