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Page 19
... vanishes and the solution is Q ( x ) = √2 p ( x ' ) G2 ( x , x ) d ° x ' Φ 1 4π J. P ( X ) aGD da ' ( 1.44 ) дп ' For Neumann boundary conditions we must be more careful . The obvious choice of boundary condition on G ( x , x ' ) seems ...
... vanishes and the solution is Q ( x ) = √2 p ( x ' ) G2 ( x , x ) d ° x ' Φ 1 4π J. P ( X ) aGD da ' ( 1.44 ) дп ' For Neumann boundary conditions we must be more careful . The obvious choice of boundary condition on G ( x , x ' ) seems ...
Page 282
... vanishes inversely as the hemisphere radius as that radius goes to infinity . Then we obtain the Kirchhoff integral for y ( x ) in region II : Y ( x ) = - 1 eikR 4π JS1 R - n . V'y ' + ik ( 1+ ) y da ' ( 9.65 ) iR KR / R where n is now ...
... vanishes inversely as the hemisphere radius as that radius goes to infinity . Then we obtain the Kirchhoff integral for y ( x ) in region II : Y ( x ) = - 1 eikR 4π JS1 R - n . V'y ' + ik ( 1+ ) y da ' ( 9.65 ) iR KR / R where n is now ...
Page 284
... vanishes identically . To do this we make use of the following easily proved identities connecting surface integrals over a closed surface S to volume integrals over the interior of S : § A⋅nda = √2v . Adz f2 S S V. V ( n x A ) da ...
... vanishes identically . To do this we make use of the following easily proved identities connecting surface integrals over a closed surface S to volume integrals over the interior of S : § A⋅nda = √2v . Adz f2 S S V. V ( n x A ) da ...
Contents
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Greens theorem | 14 |
BoundaryValue Problems in Electrostatics I | 26 |
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4-vector acceleration Ampère's law angular distribution antenna approximation atomic axis B₁ Babinet's principle behavior boundary conditions calculate Chapter charge q charged particle classical coefficients collisions component conducting conductor constant coordinate cross section cylinder d³x dielectric diffraction dimensions dipole direction discussed E₁ effects electric field electromagnetic fields electrons electrostatic energy loss energy transfer factor force equation formula frequency given Green's function impact parameter incident particle integral Kirchhoff Lorentz invariant Lorentz transformation magnetic field magnetic induction magnitude Maxwell's equations meson modes momentum motion multipole nonrelativistic obtain oscillations P₁ parallel perpendicular plane wave plasma plasma oscillations polarization power radiated Poynting's vector problem propagation quantum quantum-mechanical radius region relativistic result scalar scattering screen shown in Fig shows sin² solid angle solution sphere spherical surface transverse unit V₁ vanishes vector potential velocity wave number wavelength ΦΩ