An isolated, uncharged conducting sphere of radius is placed in a uniform applied…
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics · Conductors, capacitance and boundary-value electrostatics
The Boundary-Value Problem, Ch Separation of variables in spherical geometry
Problem
An isolated, uncharged conducting sphere of radius a=5.0cm is placed in a uniform applied field E0=2.0×105Vm−1, far from any other charge. Someone argues: "A conductor always shields its interior and weakens the field at its own surface, since free charges rearrange to oppose the applied field. So the field at the pole of the sphere, where the induced charge is densest, must be smaller than the applied field E0, not larger."
((a)) Using the surface field found for a conducting sphere in a uniform field, calculate the field just outside the sphere at the pole (θ=0) and at the equator (θ=π/2).
((b)) Say whether the quoted argument is correct, and if not, locate exactly where it goes wrong.