Classical Electrodynamics · Problem 2.9
Boundary-Value Problems in Electrostatics: II — John David Jackson
Physics — E&M · conducting-sphere-uniform-field-hemispheres
Problem
An insulated, spherical, conducting shell of radius is in a uniform electric field . If the sphere is cut into two hemispheres by a plane perpendicular to the field, find the force required to prevent the hemispheres from separating (a) if the shell is uncharged; (b) if the total charge on the shell is .Intuitive explanation
When a conductor sits in an external field, charges redistribute to make the interior field zero—but this creates surface charge density and an electric stress that tries to pull the material apart. The key is finding the electrostatic pressure (force per unit area) acting outward on the conductor surface, then integrating it across the plane that cuts the sphere. For part (b), you'll also have the self-energy stress from the shell's own charge. Think of it as: what's pushing the two halves apart, and how much force must you apply to hold them together?
Intuitive explanation
When a conductor sits in an external field, charges redistribute to make the interior field zero—but this creates surface charge density and an electric stress that tries to pull the material apart. The key is finding the electrostatic pressure (force per unit area) acting outward on the conductor surface, then integrating it across the plane that cuts the sphere. For part (b), you'll also have the self-energy stress from the shell's own charge. Think of it as: what's pushing the two halves apart, and how much force must you apply to hold them together?