Question

Problem 2. An unknown spherically symmetric distribution of charges and conducting or insulating materials extends from r = 0 to r = 2R. The electrostatic potential varies with radial distance r away from the center of the distribution as follows: For r > 2R, V (r) = −q/(4πǫ0r); for R < r < 2R, V (r) = −q/(8πǫ0R); and for r < R, V (r) = −3q/(4πǫ0r) + 5q/(8πǫ0R).

(a) Graph V (r) from r = 0 to r = 4R.

(b) Calculate the electric field Er = −dV /dr in each region and graph it from r = 0 to r = 4R.

(c) Describe a set of objects (point charges, conducting or insulating shells, etc.) that could produce an electrostatic potential that behaves this way. Describe their physical extent and the distribution of charge on each. There may be more than one answer.

Answer 1