Consider a solid, insulating sphere of radius a = 5.00 cmcarrying a net positive charge of Q = 3.00 μC uniformly distributedthroughout its volume. Concentric with this sphere is a hollow,conducting spherical shell with inner radius b = 10.0 cm and outerradius c = 15.0 cm having a net negative charge of q = -1.00μC.

a) Give the expression from Gauss’s Law for the magnitude ofelectric field inside the insulating sphere for 0 ≤ r ≤ a, and usethis expression to calculate the value of the electric field at r =0 and r = a = 5.00 cm.

b) Since the spherical shell is conducting, it contributesnothing to the electric field inside its hollow space. Give theexpression from Gauss’s Law for the magnitude of electric field fora ≤ r < b, and use this expression to calculate the value of theelectric field at r = a = 5.00 cm and r = b = 10.0 cm. (Note yourvalue here of the electric field at r = a should agree with yourresult above.)

c) From the properties of conductors in electrostaticequilibrium, what is the magnitude of the electric field inside theconducting shell for b < r < c?

d) Because of your answer above, what must be the charge on theinner surface of the hollow conducting shell?

e) Given the net charge carried by the hollow conducting shell,what must be the charge on its outer surface?

f) Using Gauss’s Law, determine the expression for the magnitudeof electric field for r > c, and use this expression tocalculate the value of the electric field at r = c = 15.00 cm and r= 25.0 cm.

g) Make a graph of the magnitude of the electric field for 0 ≤ r≤ 25.0 cm. Draw this to scale specifying your results calculatedabove.