39 dr e dl poantb nlh lii cirdrfrn de lai dl let c dt

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Unformatted text preview: face bounding volume τ. S ˆ ∫ C A • dl = ∫ (∇ × A) • n dA R= S ˆ ∫ E• n dA = Qenc / ε0 ∫ C E • dl =0 Stoke’s theorem: C is a closed curve bounding surface S. statics only B • n dA = 0 ∫ ˆ ∫ C B • dl =µ0 I enc N Φ B = Li statics only ε = − L di ε = − d Φ B dt dt Full Maxwell equations: Differential form ε0µ0 = 1 / c 2 ∇ • E = ρ / ε0 ∇•B = 0 ∂B ∇×E+ =0 ∂t 1 ∂E ∇×B− 2 = µ0 J c ∂t Full Maxwell equations: Integral form ˆ ∫ E • n dA = Qenc / ε0 ˆ ∫ B • n dA = 0 Figrr. Φ 3.9 dR E • dl = −poant!B nlh. l€ii cird€r€F!!€rn dE lai d.l ∫ Let C dt a oossibl€ oondinateim6 th.t obs€wll! in in.nial c t ftamesmovingat va.iousdiftelent velociti.s might ∂E meagllt ctvr entvro g €n event!. t€r f € + ∫ε n ∫ C B • dl =µ0 Icirdbµr0 pr€€50€ntldhoiv•€nˆod.A posiu€,oints in thim.s .ight €€ proper t t . f ll S €ent €sama6v resent me.sulEdbalwbut mhovingb€tw€n6tby cloct! palong st both t vcnt! e €€n ha cvantt r '(t ') = r (t ) − βd iff €rent oddlines. h6s inglap ointi n c ommon $ T vadous sets b€− € v '(t ') = v (t ) tveβn tthe!6Gnrr is $e spacstimeintcrvalA5 ho d b€t$€en Newtonian relativity a '(t ') = a (t ) Three kinds of time Cood|t. Ttt|. ?rop..Ift|. Th. tirP b€twen two Th€rime betwccn two .vmt6 m€asurEdin an irEri.l rEturrr? fi|me W a Fir of sy,ttuonird clocls, onc pr€l€llt at eadr ev€nt (It botl' cv€nts haPFn to (rc1lr Mnitidl Convarion l lyElbol ind€Fndcnt? GeodErrL.h.l%y sg.c.rf!. The tirE betw..n lwo €vgrts r! dE rutsd by .n ir€rtirl cLoclprtr.nt at bodr cv€rt& (8ec.u!a m instial docf fol,ows. uniqu€ worldline bctweelrthc ever*s, the spacetim€ lnlcrval'! value b uniquefor . Cv6r pai! of by . si$l€ cl,ocr p!.!srt at Mr 6Ert!. (ltt v.luc dq6d3 dr th€worldlim th.t lh€ clockfollows in tctdry ftorn oll€ €vctrtto dE otlE .) 3ingk docl suffc€s.)' AI No Worri AlErudrdy, th. @diMb 2 tr o,2tlEdEt 2 uiit <lddi tift dituEE 2 t2 r&r !.rH, E Distanae Pathlenttt Spatiaf coodimte b.ts6 2 two.e.it! Δs = Δt − Δd = Δt − Δx − Δy − Δz 2 mi8ht b. i.H Ad llExGrErt'ddErprrd!. metric equation: invariant spacetime interval tB by definition. So drc spacetimenierval befipee{r 2 i is a specirl case h ΔτaAptDFr time−rd 2 sp€cialcaseofAa c= 1 − vroΔeventsigu.lERtant) 1 d v a dt Δτ B rrodinate timeAs€ef cons 3.9). t ( B (v of B = tA TablesR3.1and R3.2summarizeand organize the ideas pr€send in this chapter.In chapter R4, we will explore the reLtionship betweenthe a coudinaie time 1nd thc spac€timeinErval betweantrvo ev€ntswith the 1 −oI 2 n≈ quatimvc2.fled iE 1 +tdc ≈ 1 + axduptcr R5,we will u5ethe v a e1 − a x help n Euttion.ln 2 link coordiME tinE to metric equalim to PtoFr time. ∫ ( β =v/c γ= 1 1 β 2 ) hb'ld Δt " = γ ( Δt − βΔx ) Δt = γ ( Δt " + βΔx") Δx" = γ (−βΔt + Δx ) Δx = γ (+βΔt " + Δx") Δy" = Δy Δz" = Δz Δy = Δy" Δz = Δz" L = LR / γ v! = x vx − β 1 − β vx vx = v! + β x 1 + β v! x v! = y vy 1 − β 2 1 − β vx vy = v! 1 − β 2 y 1 + β v! x v! = z vz 1 − β 2 1 − β vx v! 1 − β 2 vz = z 1 + β v! x ! # ! Pt , Px , Py , Pz # = %m dt , m dx , m dy , m dz & " $ " dτ dτ dτ dτ $ " Pt!% "γ ( Pt − β Px ) % ' $'$ $ Px!' = $γ (−β Pt + Px )' ' $ Py!' $ P ' $ ' $y ' $ Pz!' $ Pz #&# & E = γm p = γ mv K = E − m m 2 = E 2 − P 2 % "E! % "Ex x $ ' $' E ! ' = $γ ( E y − β Bz )' $y ' $E! ' $ # z & $γ ( Ez + β By )' # & % " B! % " Bx x $ ' $' B! ' = $γ ( By + β Ez )' $y ' $ B! ' $ # z & $γ ( Bz − β E y )' # &...
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This document was uploaded on 03/08/2014 for the course PHYS 122 at University of Washington.

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