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 The field as a differential equation: Poisson, Laplace and the well-posed problem
Problem
A closed rectangular metal box has six faces, each insulated from its neighbours by thin gaps so their potentials can differ. Five faces are earthed, and the sixth is connected to a battery and held at V0=90V. A small metal block hangs inside the box on an insulating thread; it is connected to nothing and is known to carry a total charge Q=2.0nC. The rest of the interior is vacuum and free of charge.
((a)) Classify the boundary data given on each of the six faces and on the surface of the block: Dirichlet, Neumann, or the third kind used for an isolated conductor of known charge.
((b)) Write the one equation that stands in for a stated potential on the block's surface.