Classical Electrodynamics · Problem 1.19

Boundary-Value Problems in Electrostatics: I — John David Jackson

Physics — E&M · cylindrical-capacitor-variational-bound

Problem

For the cylindrical capacitor of Problem 1.6c, evaluate the variational upper bound of Problem 1.17b with the naive trial function, Ψ1(ρ)=(b−ρ)/(b−a)\Psi_1(\rho) = (b - \rho)/(b - a). Compare the variational result with the exact result for b/a=1.5,2,3b/a = 1.5, 2, 3. Explain the trend of your results in terms of the functional form of Ψ1\Psi_1. An improved trial function is treated by Collin (pp. 275--277).

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