A conducting spherical shell with inner radius a and outer radius b has a positive - 22.42

22.42 • A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is −3Q, and it is insulated from its surroundings (Fig. P22.42). (a) Derive expressions for the electric-field magnitude E in terms of the distance r from the center for the regions r a, a r b, and r b. What is the surface charge density (b) on the inner surface of the conducting shell; (c) on the outer surface of the conducting shell? (d) Sketch the electric field lines and the location of all charges. (e) Graph E as a function of

A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is −3Q, and it is insulated from its surroundings (Figure 1).
Derive the expression for the electric field magnitude in terms of the distance r from the center for the region r a.
In the region r a, in which direction does the electric field vector point?
Derive the expression for the electric field magnitude in terms of the distance r from the center for the region a r b.
Derive the expression for the electric field magnitude in terms of the distance r from the center for the region r b.
In the region r b, in which direction does the electric field vector point?
What is the surface charge density on the inner surface of the conducting shell?
What is the surface charge density on the outer surface of the conducting shell?

Problem from University Physics with Modern Physics