express the following three-dimensional charge densities p(r) in terms of products of one-dimensional Dirac delta functions in the individual coordinates: (a) In spherical coordinates, a charge Q uniformly distributed over a spherical shell of radius R. (b) In cylindrical coordinates, a charge A per unit length uniformly distributed over a cylin- drical surface of radius b. (c) In cylindrical coordinates, a charge Q spread uniformly over a flat circular disc of negligible thickness and radius R. (d) The same as (c), but using spherical coordinates.

express the following three-dimensional charge densities p(r) in terms of products of one-dimensional Dirac delta functions in the individual coordinates: (a) In spherical coordinates, a charge Q uniformly distributed over a spherical shell of radius R. (b) In cylindrical coordinates, a charge A per unit length uniformly distributed over a cylin- drical surface of radius b. (c) In cylindrical coordinates, a charge Q spread uniformly over a flat circular disc of negligible thickness and radius R. (d) The same as (c), but using spherical coordinates.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.36P

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