Question

2) We can model the earth as a solid spherical conductor of radius RE surrounded by a concentric spherical conducting shell with inner radius Ri , and outer radius Ro, which is the ionosphere. The earth has charge +Q, while the ionosphere has zero net charge. Write all answers in terms of Q, RE, Ri , Ro, and 0.

For parts (a) through (c), what is the surface charge density on

(a) the outer surface of the inner sphere of radius RE?

(b) the inner surface on the spherical shell at radius Ri?

(c) the outer surface of the spherical shell at radius Ro?

For parts (d) through (g), determine the electric field E(r) everywhere in space:

(d) r < RE

(e) RE < r < Ri

(f) Ri < r < Ro

(g) r > Ro

(h) Calculate the energy of the system.

(i) Determine the potential at the center given that the potential is zero at r = ∞.

(j) Find the capacitance of the earth-ionosphere system assuming that the ionosphere has net charge −Q instead of zero.

Answer 1