A point charge with a charge of -3Q is placed at the center of a conducting spherical shell. The shell has an inner radius a, an outer radius b, and a net charge of +2Q.
What is the electric field as a function of r?
For r > b, E = kQ/r2 and points toward the center
For a < r < b, E = 0
For r < a, E = 3kQ/r2, directed toward the center
What is the electric potential as a function of r?
To find the total potential we can simply use superposition. The net potential is the potential from the different pieces, the point charge, the +3Q charge on the inner surface of the conductor, and the -Q on the outer surface of the conductor.
|Region||Point Charge|| Conductor |
|r > b||-3kQ/r||+3kQ/r||-kQ/r||-kQ/r|
|a < r < b||-3kQ/r||+3kQ/r||-kQ/b||-kQ/b|
|r < a||-3kQ/r||+3kQ/a||-kQ/b||-3kQ/r + 3kQ/a - kQ/b|