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... obtained from this expansion . If we let x ' → · 0 , only the m = O term survives , and we obtain the integral representation : 1 2 ∞ cos kz Ko ( kp ) dk 2 + z2 == π JO 12 ( 3.150 ) If we replace p2 in ( 3.150 ) by R2 = p2 + p'2 - 2pp ...
... obtained from this expansion . If we let x ' → · 0 , only the m = O term survives , and we obtain the integral representation : 1 2 ∞ cos kz Ko ( kp ) dk 2 + z2 == π JO 12 ( 3.150 ) If we replace p2 in ( 3.150 ) by R2 = p2 + p'2 - 2pp ...
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... obtain the result : π ( E1 + m2 ) m2E1 m2 ( m2E m12 + m22 + m2 2 2 ms 2 ± p cos 02 [ ( m2E1 + m‚2 + m ̧2 — m22 — m‚2 ) 2 2 2 - - m32m2 - p2m2 sin2 0 , E3 ( 12.53 ) 2 ( E1 + m2 ) 2 — p2 cos2 03 Only the values of ( 12.53 ) greater than m ...
... obtain the result : π ( E1 + m2 ) m2E1 m2 ( m2E m12 + m22 + m2 2 2 ms 2 ± p cos 02 [ ( m2E1 + m‚2 + m ̧2 — m22 — m‚2 ) 2 2 2 - - m32m2 - p2m2 sin2 0 , E3 ( 12.53 ) 2 ( E1 + m2 ) 2 — p2 cos2 03 Only the values of ( 12.53 ) greater than m ...
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... obtain e21⁄4 / 4 -In v2 ω 00 iwt 1- ( 1–1.7 ) d ( ) _ 22 a x vi2 | ~ ~ ( ~~ • ~ • ) dt | * ( 14.127 ) ΦΩ = c3 2π S The integral is a Dirac delta function . Then dI ( w ) e2ep2 sin2 0 = ΦΩ с - | 8 ( 1 − eß cos 0 ) | 2 ( 14.128 ) where ...
... obtain e21⁄4 / 4 -In v2 ω 00 iwt 1- ( 1–1.7 ) d ( ) _ 22 a x vi2 | ~ ~ ( ~~ • ~ • ) dt | * ( 14.127 ) ΦΩ = c3 2π S The integral is a Dirac delta function . Then dI ( w ) e2ep2 sin2 0 = ΦΩ с - | 8 ( 1 − eß cos 0 ) | 2 ( 14.128 ) where ...
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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