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 spherical capacitor consists of two concentric, thin conducting shells in vacuum: an inner shell of radius s1=2.0cm held at potential V0=150V, and an outer shell of radius s2=6.0cm connected to earth (V=0). There is no free charge in the vacuum gap between the shells.
((a)) Write down the region Ω, the differential equation holding in Ω, and the boundary data on each of its two bounding surfaces.
((b)) Classify the boundary condition on each surface as Dirichlet, Neumann or mixed, and say whether the resulting problem is well posed as defined for a bounded region.