homework_12_solution

homework_12_solution - q d − R 0 V i + Ri V 0 qd −Vi...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: q d − R 0 V i + Ri V 0 qd −Vi /V0 + Ri /R0 [= [(R0 V0 ) R · V dτ R·V R · V dτ R·V ˙ ˙ ˆ ˆ ˆ ˆ ˆ ˆ Ri − β i q d Ri − β i qγ Ri − β i ˙ ˙ ˆˆ ˆˆ = [= [ − (−R · β − R · β )] ˆˆ ˆˆ ˆˆ R · V dτ 1 − R · β R · V (1 − R · β ) (1 − R · β )2 qγ ˙ ˙ ˙ ˙ ˙ ˆ ˆˆ ˆ ˆˆˆ ˆˆˆ ˆ ˆ ˆˆ ˆ ˆ = [(−β i + β i R · β + (Ri − β i )R · β ) + (Ri − Ri R · β + (Ri − β i )R · β )] ˆˆ R · V (1 − R · β )2 Fi 0 = ˙ ˙ ˙ ˙ ˙ ˆ ˆˆ ˆ ˆˆˆ ˆˆˆ ˆ ˆ ˆ ˆ ˆˆ ˆ ˆ ˆˆ −β i + β i R · β + ( R i − β i )R · β = −R · (R − β )β i + ( R i − β i )R · β = R × (R − β ) × β cˆ ˙ ˆ ˆ R i = − (β i − R i ) R0 ˆ ˆ c c(R i − β i ) ˙ ˙ ˙ ˆˆˆ ˆˆˆ ˆ ˆ ˆˆ ˆ ˆ Ri − Ri R · β + (Ri − β i )R · β = (1 − β · β )(Ri − β i ) = R0 γ 2 R0 ˆ ˆ c( R i − β i ) ˙ ˆ ˆ ˆˆ + R × (R − β ) × β ] 2R ˆ ˆ · β )2 γ0 R · V (1 − R qγ c qγ ˙ ˆ ˆ ˆ ˆ ˆˆ = (R i − β i ) + [R × (R − β ) × β ] 2 ˆˆ ˆˆ R0 V0 γ 2 (1 − R · β )3 R0 V0 (1 − R · β )3 q q ˙ ˆ ˆ ˆ ˆ ˆˆ = (R i − β i ) + [R × (R − β ) × β ] 2 γ 2 (1 − R · β )3 ˆˆ ˆˆ R Rc(1 − R · β )3 Fi 0 = qγ [ qγ ˙ ˙ ˙ ˙ ˙ ˙ ˆˆ ˆˆ ˆˆ ˆ ˆ ˆˆ ˆ ˆ ˆˆˆ ˆ ˆˆˆ ˆ {[Ri βj − Rj βi + Ri βj (R · β ) − Rj βi (R · β ) − Ri βj R · β + Rj βi R · β ] ˆˆ R · V (1 − R · β )2 ˙ ˙ ˙ ˙ ˙ ˙ ˆˆ ˆˆ ˆˆ ˆ ˆ ˆˆ ˆ ˆ ˆˆˆ ˆ ˆ ˆˆ ˆ + [ β i R j − β j R i + β j Ri ( R · β ) − β i Rj ( R · β ) − R i β j β · R + R j β i β · R ] } qγ cˆˆˆ ˙ ˆ ˆ ˆˆ = {− R × β + R × [R × (R − β ) × β ]}k ￿ijk ˆ ˆ · β )2 R0 γ 2 R · V (1 − R Fij = ￿ ˆ￿ B =R×E ￿ ￿ φ R ￿ OP P￿ ￿ P ￿ E= ￿ E= (r 2 ￿ OP ￿ ￿ ￿ OP r ￿ ￿ P￿P θ ￿ OP ￿ q γ￿ r q γ￿ r q￿ r = = 32 (1−β 2 ) sin2 θ +cos2 θ 3/2 2 γ 2 cos2 θ ) sin θ + r r γ (1 − β 2 sin2 θ)3/2 r3 ( ) 1− β 2 2 q￿ r r3 γ 2 (1 − 2 β 2 R2 r sin 2 φ ) 3/2 = q￿ r γ 2 (r 2 − β 2 R2 sin2 φ)3/2 q￿ r q￿ r =23 γ R (1 + β 2 cos2 φ − 2β cos φ)3/2 γ 2 (R2 (1 + β 2 ) − 2β R2 cos φ − β 2 R2 sin2 φ)3/2 q￿ r =23 γ R (1 − β cos φ)3 = ˆˆ q R−β ￿ E= 2 2 (1 − β · R)3 ˆˆ Rγ 2 Z 2 e2 dV 2 | | 3 c3 m2 dr Ptotal = ˆ 2 Z 2 e2 dV 2 dt 2 Z 2 e2 dV 2 W = dt(2 · | | )= · dr(2 · | |) 3 c3 m2 dr dr 3 c3 m2 dr ˆ∞ 4 Z 2 e2 dV 2 dr = 32 | |￿ 3c m 0 dr 2 [V − V (r)] ˆ min m dV Z ￿ Ze2 V =− 2 =− dr r r W = = 4 Z 2 e2 3 c3 m2 ￿ 4 Ze2 3 c3 m2 Z ￿ a V 2 dV m 2 ˆ ￿ m 16 ( ) 2 15 2 0 ￿ 2 mv0 2 −V 2 mv0 5/2 = 5 8 Zmv0 45 Z ￿ c3 ...
View Full Document

This note was uploaded on 12/29/2011 for the course PHYSICS 606 taught by Professor Bedaque during the Spring '11 term at Maryland.

Ask a homework question - tutors are online