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phys documents (dragged) 62 - 56 Physics Formulary by ir....

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56 Physics Formulary by ir. J.C.A. Wevers 11.3.2 The Coulomb interaction For the Coulomb interaction holds: 2 b 0 = q 1 q 2 / 2 πε 0 mv 2 0 , so W ( r )=2 b 0 /r . This gives b = b 0 cot( 1 2 χ ) and I ( Ω = b sin( χ ) b ∂χ = b 2 0 4sin 2 ( 1 2 χ ) Because the infuence o± a particle vanishes at r = λ D holds: σ = π ( λ 2 D - b 2 0 ) . Because dp = d ( mv )= mv 0 (1 - cos χ ) a cross section related to momentum trans±er σ m is given by: σ m = ± (1 - cos χ ) I ( Ω ) d Ω =4 π b 2 0 ln ² 1 sin( 1 2 χ min ) ³ =4 π b 2 0 ln ² λ D b 0 ³ := 4 π b 2 0 ln( Λ C ) ln( v 4 ) v 4 where ln( Λ C ) is the Coulomb-logarithm . For this quantity holds: Λ C = λ D /b 0 =9 n ( λ D ) . 11.3.3 The induced dipole interaction The induced dipole interaction, with ± p = α ± E , gives a potential V and an energy W in a dipole ²eld given by: V ( r )= ± p · ± e r 4 πε 0 r 2 ,W ( r )= - | e | p 8 πε 0 r 2 = - α e 2 2(4 πε 0 ) 2 r 4 with b a = 4 ´ 2 e 2 α (4 πε 0 ) 2 1 2 mv 2 0 holds: χ = π - 2 b ± r a dr r 2 µ 1 - b 2
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