A long coaxial cable has an outer conductor of radius connected to a battery so that…

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 long coaxial cable has an outer conductor of radius s2=5.0 cms_2 = 5.0\,\mathrm{cm} connected to a battery so that it is held at V0=100 VV_0 = 100\,\mathrm{V}. The inner conductor, of radius s1=1.5 cms_1 = 1.5\,\mathrm{cm}, is not connected to anything; it is isolated and known to carry a total charge per unit length λ=−3.0 nC m−1\lambda = -3.0\,\mathrm{nC\,m^{-1}}. The region between the conductors is vacuum and free of charge. ((a)) Name the region and the equation VV satisfies in it. ((b)) Classify the boundary data given on the outer conductor's surface and on the inner conductor's surface (Dirichlet, Neumann, or the third kind used for an isolated conductor of known charge). ((c)) Write the one extra equation available on the inner surface in place of a stated potential.

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