(C 17) , E to B; Lorentz Force Law: fields and forces (C 17) Lorentz Force Law: currents
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1 Mn. Wd Thus. Fi. ( 7)..-..,.3. t ; Lnt F Law: filds and fs ( 7) 5..3 Lnt F Law: unts ( 7) 5. it-saat Law HW6
2 F Q F btwn statina has Q F Q (ulb s Law: n.) Q Q Q ˆ Q 3 F btwn in has V ˆ 3 u ( n 0.7) V Q a u u a u u a u ˆ Th nti th f lassial ltdnais is ntaind in that uatin but u s wh I pfd t stat ut with ulb s law. - Giffiths
3 F btwn in has Nt: tl asti btwn tw has; ipit (Nwtn s 3 d ) ds nt hld V Q a F Q u F Q = Q πε u 3 u + u a + V u + u a lti Dpnds n bs s pptin f su ha s lit and alatin Manti Als dpnds n bs s pptin f ipint ha s lit ut wh s in hw fast is all lati
4 ash us in Spial Rlatiit Pinipl: Laws f Phsis shuld b th sa in all intial fas f fn ball u ball u Old fa-tansfatin ath: t ball u ball u Obsatins: laws f &M fnd an abslut spd, nt spd lati t pfd fa ha in na statina ant fls anti f; ha statina na in ant fls? On f th th ust K t nw fa-tansfatin ath: Spd f liht is asud t b th sa in all fn fas
5 ash us in Spial Rlatiit Nw fa-tansfatin ath did liht lks and t stiks with lk t w. = h Masud in fa at st with tw nts dfinin intal h d = h + L = h + t w.s w.s = t w. + t w.s L w. = t w. L w. = t w.s L w. = L w. s L w.s = t w.s With t stik Masud in fa at st with tw latins f dfinin nts. L w. tw. d t w.s t w.s = t w. + t w.s t w.s = t w. + t w.s t w.s = t w. + t w.s t w.s = t w. L w. s = L w. lk s pp ti: = L w. : Stik s pp lnth t w. = t w.s Ain abut bth and ans disain abut t and L. = γ t w.s
6 L w. s = ash us in Spial Rlatiit Nw fa-tansfatin ath did liht lks and t stiks apl L w. = L w. t w. = t w.s = γ t w.s Think f th ladd and ban pbl. Sa th Fa s t hld f th ladd and h s in t un at th ban.
7 ash us in Spial Rlatiit Galilan Tansfatin td ball.tabl I in a tain wathin a pl a. I s th ball l a distan t th pkt. I s it s takin ti t ball.tabl t t th. Manwhil, th tain and I a llin thuh th statin in th sa ditin at spd. Yu, standin in th statin, s all this happn. lassiall, u d iain that with ad stik, I d asu th ball llin a distan " ball.tabl " = ball. statin- t ball.statin ut t phas that in ts f what I in th tain wuld asu, " ball.tabl " = γ ball.tabl s,, γ ball.tabl = ball. statin- t ball.statin ball. tabl = - t ball.statin ball. statin) Thn aain, I d iain with u adstik u d asu th ball llin a distan " ball.statin " = ball. tabl + t ball.tabl ut in ts f what u in th statin wuld asu, " ball.statin " = γ ball.statin s, ball. statin = ball. tabl + t ball.tabl ) Nt: bth bss asu nsistnt nl if t ball.statin = t ball. tabl + distans as pp lnths ball. tabl) f thi stiks, but nith is a t ball. tabl = t - uidistant t th tw ntsnith asus pp ball.statin ball. statin) ti
8 ash us in Spial Rlatiit Galilan Tansfatin td ball.tabl I in a tain wathin a pl a. I s th ball l a distan t th pkt. I s it s takin ti t ball.tabl t t th. Manwhil, th tain and I a llin thuh th statin in th sa ditin at spd. Yu, standin in th statin, s all this happn. ball.statin = ball.statin t ball.statin = γ ball.tabl + t ball.tabl γ t ball.tabl + ball.tabl S alba lat, O nain = tabl.statin ball. statin = ball. tabl + + ball. tabl ball. statin = ball. tabl + tabl. statin + tabl.statin ball.tabl
9 ash us in Spial Rlatiit Nw fa-tansfatin ath did liht lks and t stiks apl ball. statin = ball. tabl + tabl. statin + tabl.statin ball.tabl
10 Tansitin / Tansfatin f t M Lab fa: u and I s an ltiall nutal wi (all b it, with th ltns in) l l lab lab l + = ins ha dnsit l - =l + = ltns ha dnsit (ulbs/t) (ulbs/t) Mtal wi = ini ati = ltn = ltn lit asud b us in th lab fa Statina ha F wi wi wi l l l l 0
11 Tansitin / Tansfatin f t M Lab fa: u and I s an ltiall nutal wi (all b it, with th ltns in) l l lab lab l + = ins ha dnsit l - =l + = ltns ha dnsit (ulbs/t) (ulbs/t) = ini ati = ltn = ltn lit asud b us in th lab fa Min ha F wi?
12 Tansitin / Tansfatin f t M ha s fa: hain f psiti ats in bakwads at S spain sn b ha is latd t thi statina, pp spaatin (as sn in lab) b ats hain f ltns in fwad at nl lab pp at at. lab lab l Siilal, spaatin in lab fa lats t pp spaatin (sn in ltns st fa) lab pp. O ha dnsit appas pssd t S spain sn b ha is latd t thi statina, pp spaatin (nt sn in lab) b pp. wh wh bind: lab S, lab l l
13 l + = ins ha dnsit (ulbs/t) Tansitin / Tansfatin f t M = ltn lit asud b ha l - = ltns ha dnsit (ulbs/t) ha s fa: - lab l l lab l wi wi F wi l l l l l wh A bit f alba lat, wi l l Dfin and I l wi I s wi I F Hand wain: F~ distan/ti Tansfatin f st fa uis fat f / / I F wi Finall, w bs:
14 F Q = Q πε Jupin in t Mantis u 3 u + u a + V u + u a lti Dpnds n bs s pptin f su ha s lit and alatin Manti Als dpnds n bs s pptin f ipint ha s lit u Manti f F Q.a =QV πε u 3 u + u a Manti Fild, F Q.a =QV
15 dp d ltn Mtin in a Unif Manti Fild d d d d d d d F d ˆ ˆ Tak nt diati ss substitut d d d In nal ˆ d pa ts and nlud 3 Guss Slutin Fs k s apl t st sint t t sint 3 s d Plu in sin t st st sint 3
16 ltn Mtin in a Unif Manti Fild F t t sint t t st s sin wh F psitin pnnts, intat k s apl t sin t s t 5 t st sint t Ips Initial nditins Stat at iin t sint st t s t sint t
17 ltn Mtin in a Unif Manti Fild F t t sint t t st s Initial psitin: (0,0) sin wh Ips Initial nditins k s apl t sint st t s t sint t Initial Vlit: s0 sin0 0 sin0 s0 0 0 S. 0 0 t sint t st t st t t sint
18 ltn Mtin in a Unif Manti Fild F t t sint t t st s Initial psitin: (0,0) sin wh k s apl t sint st t s t sint t Initial Vlit: 0 / ˆ 0 s0 sin0 0 0 Ips Initial nditins sin0 s0 0 0
19 Mn. Wd Thus. Fi. ( 7)..-..,.3. t ; Lnt F Law: filds and fs ( 7) 5..3 Lnt F Law: unts ( 7) 5. it-saat Law HW6
20
21 ltn Mtin in a Unif Manti Fild d d d F a F Q Q d d Siilal f : d dp d d d d F a ˆ t sint t sint ( t) 3 s ( t) s ˆ ˆ F sin t s t s t sint 3 3 Plu in t ˆ
22 ltn Mtin in a Unif Manti Fild F a F Q t sint ( t) s t sint ( t) s Intat f psitins: Q t d ( t) t sin t s t siilal: t sint s t
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