Introduction to Electrodynamics · Problem 2.60
Electrostatics — David J. Griffiths
Physics · work-moving-charge-through-shell
Problem
A point charge is at the center of an uncharged spherical conducting shell, of inner radius and outer radius . Question: How much work would it take to move the charge out to infinity (through a tiny hole drilled in the shell)?Intuitive explanation
The key is recognizing that the conducting shell responds to the central charge by developing induced charges on its inner and outer surfaces—and these induced charges create their own electric potential that you must work against. The inner surface attracts charge (canceling the field inside the conductor), while the outer surface develops (restoring the external field). You're not just escaping the central charge; you're also pulling away from the attractive induced charge on the inner surface, which does real work on you. Calculate the potential energy of interaction between and each induced charge distribution, then find the work needed to disassemble the system.
Intuitive explanation
The key is recognizing that the conducting shell responds to the central charge by developing induced charges on its inner and outer surfaces—and these induced charges create their own electric potential that you must work against. The inner surface attracts charge (canceling the field inside the conductor), while the outer surface develops (restoring the external field). You're not just escaping the central charge; you're also pulling away from the attractive induced charge on the inner surface, which does real work on you. Calculate the potential energy of interaction between and each induced charge distribution, then find the work needed to disassemble the system.