A System to convert Gravitational Energy directly into Electrical Energy

Size: px

Start display at page:

Download "A System to convert Gravitational Energy directly into Electrical Energy"

Liliana Manning
6 years ago
Views:

1 A Syst to covt avitatioal Ey dictly ito Elctical Ey Fa D Aquio Maahao Stat Uivsity, Physics Datt, S.Luis/MA, Bazil. Coyiht by Fa D Aquio. All Rihts Rsvd. W show that it is ossibl to oduc sto avitatioal acclatios o th lctos o a coducto i od to obtai lctical cut. This allows th covsio o avitatioal y dictly ito lctical y. H, w oos a syst that ca oduc sval ts o kilowatts o lctical y covtd o th avitatioal y. Ky wods: Modiid thois o avity, Elctic ilds cts o atial lows, Elcto tubs, Elctical istuts. PACS:.5.Kd, 8.6.N, 8.7.+w, Itoductio I a vious a [], w hav oosd a syst to covt avitatioal y ito otatioal kitic y (avitatioal Moto), which ca b covtd ito lctical y by as o a covtioal lctical ato. Now, w oos a ovl syst to covt avitatioal y dictly ito lctical y. It is kow that, i so atials, calld coductos, th lctos a so loosly hld by th ato ad so clos to th ihboi atos that thy td to dit adoly o o ato to its ihboi atos. This as that th lctos ov i all dictios by th sa aout. Howv, i so outsid oc acts uo th lctos thi ovt bcos ot ado, ad thy ov o ato to ato at th sa dictio o th alid oc. This low o lctos (thi lctic cha) thouh th coducto oducs th lctical cut, which is did as a low o lctic cha thouh a diu []. This cha is tyically caid by ovi lctos i a coducto, but it ca also b caid by ios i a lctolyt, o by both ios ad lctos i a lasa []. Thus, th lctical cut aiss i a coducto wh a outsid oc acts uo th lctos. This oc is calld, i a ic way, o lctootiv oc (EMF). Usually, it is o lctical atu ( F E). H, it is show that th lctical low ca also b achivd by as o avitatioal ocs ( F ). Th avitatioal Shildi Ect (BR Patt Nub: PI856-5, July, 8 []), shows that a batty o avitatioal Shildis ca stoly itsiy th avitatioal acclatio i ay dictio ad, i this way, it is ossibl to oduc sto avitatioal acclatios o th lctos o a coducto i od to obtai lctical cut.. Thoy Fo th quatizatio o avity it ollows that th avitatioal ass ad th itial ass i a colatd by as o th ollowi acto []: Δ χ + i i c () wh i is th st itial ass o th aticl ad Δ is th vaiatio i th aticl s kitic otu; c is th sd o liht. Wh Δ is oducd by th absotio o a hoto with wavlth λ, it is xssd by Δ h λ. I this cas, Eq. () bcos

2 i h ic + λ λ + λ wh λ h ic is th D Boli wavlth o th aticl with st itial ass i. It has b show that th is a additioal ct - avitatioal Shildi ct - oducd by a substac whos avitatioal ass was ducd o ad ativ [5]. Th ct xtds byod substac (avitatioal shildi), u to a ctai distac o it (alo th ctal axis o avitatioal shildi). This ct shows that i this io th avity ( ) acclatio,, is ducd at th sa ootio, i.., χ wh χ i ad is th avity acclatio bo th avitatioal shildi). Cosqutly, at a scod avitatioal shildi, th avity will b iv by χ χ χ, wh χ is th valu o th atio i o th scod avitatioal shildi. I a alizd way, w ca wit that at th th avitatioal shildi th avity,, will b iv by χ χ χ... χ ( ) This ossibility shows that, by as o a batty o avitatioal shildis, w ca ak aticls acqui oous acclatios. I actic, this ca lad to th coctio o owul aticls acclatos, kitic waos o waos o shockwavs. Fo Elctodyaics w kow that wh a lctoatic wav with qucy ad vlocity c icids o a atial with lativ ittivity ε, lativ atic ability μ ad lctical coductivity σ, its vlocity is ducd to v c wh is th idx o actio o th atial, iv by [ 6] c ε μ + ωε + v I σ >> ωε, ω π, Eq. () ducs to μ σ πε ( σ ) ( ) () 5 Thus, th wavlth o th icidt adiatio (S Fi. ) bcos λ od v c v λ c/ c λ π μσ v c/ λ od v/ c/ Fi. Modiid Elctoatic Wav. Th wavlth o th lctoatic wav ca b stoly ducd, but its qucy ais th sa. ( 6) I a laia with thickss qual toξ cotais atos/, th th ub o atos aa uit is ξ. Thus, i th lctoatic adiatio with qucy icids o a aa S o th laia it achs S ξ atos. I it icids o th total aa o th laia, S, th th total ub o atos achd by th adiatio is N S ξ. Th ub o atos uit o volu,, is iv by S N ρ A 6 ( 7) wh N 6. atos / kol is th Avoado s ub; ρ is th att dsity o th laia (i k/ ) ad A is th ola ass(k/kol). Wh a lctoatic wav icids o th laia, it stiks N ot atos, wh N ( S ) φ, φ is th diat o th ato. Thus, th lctoatic wav icids ctivly o a aa S N S, wh πφ is th coss sctio aa o o ato.

3 At ths collisios, it cais out with th oth atos (S Fi.). collisios total hotos N collisios P h ( S ) () ξ l Substitutio o Eq. () ito Eq. () yilds ato S Wav Fi. Collisios isid th laia. Thus, th total ub o collisios i th volu Sξ is N collisios N + Sξ l collisios Sφ + l ( Sξ Sφ ) Th ow dsity, D, o th adiatio o th laia ca b xssd by P D S l N P S () 8 () 9 W ca xss th total a ub o collisios i ach ato,, by as o th ollowi quatio total hotos N N collisios ( ) Sic i ach collisio a otu h λ is tasd to th ato, th th total otu tasd to th laia will b Δ ( N ) h λ. Tho, i accodac with Eq. (), w ca wit that () l + () i l + total ( N) hotos λ λ N collisios λ λ ( ) () l P λ + () l Sξ i l h λ ( ) ( ) Substitutio o P iv by Eq. (9) ito Eq. () ivs () l N SD lsξ + () () i l i l c λ Substitutio o N ( l S ) φ ito Eq. () sults ( ) ad S N S () l l S Sφ ξd + ( 5) () i l i () l c λ wh i () l ρ() l V() l. Now, cosidi that th laia is isid a ELF lctoatic ild with E ad B, th w ca wit that [7] () l E D μ c Substitutio o Eq. (6) ito Eq. (5) ivs () () l l l S Sφ ξe + () i l μ i() l c λ I th cas i which th aa ( 6) is just th aa o th coss-sctio o th laia w obtai o Eq. (7), cosidi that i () l ρ() l S α ξ, th ollowi xssio S ( 7) ( S α ), Sic Eq. (8) ivs N collisios Sξ, w t l

4 () () l l l Sα Sφ E + () i l μρ () l c λ I th lctical coductivity o th laia, σ () l, is such that σ () l >> ωε, th th valu o λ is iv by Eq. (6), i.., ( 8) π λ λod ( 9) μσ Substitutio o Eq. (9) ito Eq. (8) ivs 6 () l () l l Sα Sφ σ () l E + i () l 6πμ () ρ l c Not that E E siωt.th ava valu o E is qual to E bcaus E vais siusoidaly ( is th axiu valu E o E ). O th oth had, E s E. Cosqutly w ca cha E by E s, ad th quatio abov ca b witt as ollows () l χ i () l 6 () l l Sα Sφσ () l Es + 6 () πμ ρ l c Now cosid th syst show i Fi.. It was dsid to covt avitatioal Ey dictly ito Elctical Ey. Thus, w ca say that it is a avitatioal EMF Souc. Isid th syst th is a dilctic ( ) ( ) tub ( ε ) with th ollowi chaactistics: 5 α 8(diat), Sα πα 5.. Isid th tub th is a Lad sh ( ρ s K / ) with adius ad ass M s. k. Th tub is illd with ai at abit tatu ad at. Thus, isid th tub, th ai dsity is ρ ai. k. ( ) Th ub o atos o ai (Nito) uit o volu, ai, accodi to Eq.(7), is iv by Nρai 5 ai 5.6 atos/ ( ) AN Th aalll tallic lats (), show i Fi. a subjctd to dit do voltas. Th two sts o lats (D), lacd o th xts o th tub, a subjctd to V( D ) s. 87 kv at 6Hz, whil th ctal st o lats (A) is subjctd to V( A ) s kv at 6Hz. Sic d, th th itsity o th lctic ild, which asss thouh th 6 cylidical ai laias (ach o with 5 thickss) o th two sts (D), is 5 E( D ) s V( D) s d.78 V / ad th itsity o th lctic ild, which asss thouh th 9 cylidical ai laias o th ctal st (A), is iv by 5 E( A ) s V( A) s d 5.59 V / Not that th tallic is (5 thickss) a ositiod i such way to block th lctic ild out o th cylidical ai laias. Th objctiv is to tu ach o o ths laias ito a avity Cotol Clls (CC) [5]. Thus, th syst show i Fi. has sts o CC. Two with 8 CC ach, ad o with 9 CC. Th two sts with 8 CC ach a ositiod at th xts o th tub (D). Thy wok as avitatioal dclato whil th oth st with 9 CC (A) woks as a avitatioal acclato, itsiyi th avity acclatio oducd by th ass M s o th Lad sh. Accodi to Eq. (), this avity, th 9 at th 9 CC bcos 9 χ Ms, wh χ () l i() l iv by Eq. () ad 9 is th distac btw th ct o th Lad sh ad th suac o th ist CC o th st (A). Th objctiv o th sts (D), with 8 CC ach, is to duc stoly th valu o th xtal avity alo th axis o th tub. I this cas, th valu o th xtal 8 avity, xt, is ducd by th acto χd xt, wh χ d. Fo xal, i th bas BS o th syst is ositiod o th Eath

5 5 d α8 Dilctic tub ε ξ 5 at K E D(s) Lad sh (8 diat) D 7 8 E Mtallic i (5 thickss) Paalll lat caacito () Elctic ild o caacito 9 M.87kV 6Hz Io od (8 diat, hiht) F +F +F Σ F E A(s) x B A 8 9 B.5 T 7.87kV 6Hz i s 58.6A, # AW.kV 6Hz + Iducto tu (i adius: 5) T Aluiu Cabl 5AW V 6Hz 8.9 kw D 7 8 BS 5Ω 8W V μhz i A # AW N tus N s tus Nuclus μ 6 (io cast) Rlay Iitializatio souc ~ Covt 6Hz / μhz Taso Fi. A avitatioal EMF Souc (Dvlod o a ocss attd i July, 8, PI856-5)

6 suac, th to χ 8 d xt xt 9.8 / s is ducd ad, at th st A, it is icasd 9 by χ. Sic th syst is dsid o χ 6.8, th th avity acclatio o th sh bcos 9 8 χ χ. / s, this valu is uch d xt sall tha 8 sh Ms s.7 / s. Th lctical coductivity o ai, isid th dilctic tub, is qual to th lctical coductivity o Eath s atosh a th lad, whos ava valu is σ ai S / [8]. This valu is o udatal iotac i od to obtai th covit valus o th lctical cut i ad th valu o χ ad χ d, which a iv by Eq. (), i.., 6 ( ai) aisα Sφσ aie( A) s χ + 6πμ ρaic [ +.65 E( A) s ] { } ( ) χd + 6 S ( ai) ai α ai ( ) 6πμρ c [ +.65 E( D) s ] { } ( 5) wh ( ) μ ai 5 S φ σ ED s ai ε, sic ( ωε ) σ << ; ai 5.6 atos/, φ.55, S πφ.88 ad 6Hz. Sic E E 5 ( A ) s 5.59 V / 5 ( D ) s.78 V / ad χ 6.8 χ d, w t ad ( 6) ( 7) Not that th is a uio atic ild, B, thouh th Io od. Th, th avitatioal ocs du to th avitatioal ass o th sh ( s ) ), otos ( ) ( F M acti o lctos F o th F ad utos ( ) Io od, a sctivly xssd by th ollowi latios F F a a M 7 χ B χ χ B s M 7 χ s 6 ( 8) ( 9) M 7 s F a χ B χ Th actos χ B a du to th lctos, otos ad utos a isid th atic ild B. I od to ak ull th sultat o ths ocs i th Io (ad also i th sh) w ust hav F F + F, i.., χ χ + χ B B B ( ) ( ) It is iotat to ot that th st with 9 CC (A) caot b tud o bo th atic ild B is o. Bcaus th avitatioal acclatios o th Io od ad Lad sh will b oous 9 6 ( χ M s 5. / s ), ad will xlod th dvic. Th oc F is th lctootiv oc (EMF), which oducs th lctical cut. H, this oc has avitatioal atu. Th cosodi oc o lctical atu is F E. Thus, w ca wit that a E ( ) Th lctos isid th Io od (S Fi. ) a subjctd to th avity acclatio oducd by th sh, ad icasd by th 9 CC i th io (A). Th sult is M 9 9 s a χ s χ Coai Eq. () with Eq.(), w obtai M 9 s E χ Th lcto obility, μ, cosidi vaious scatti chaiss ca b obtaid by solvi th Boltza quatio i th laxatio ti aoxiatio. Th sult is [9] ( ) ( )

7 τ μ ( 5) wh τ is th ava laxatio ti ov th lcto is ad is th avitatioal ass o lcto, which is th ctiv ass o lcto. Sic τ ca b xssd by τ σ [], th Eq. (5) ca b witt as ollows σ μ Thus, th dit vlocity will b xssd by σ M 9 s vd μe χ ad th lctical cut dsity xssd by M 9 s j ρ qvd σ io χ ( 8) wh ρ q, ad χ B. Tho, Eq. (8) ducs to M 9 s j σ io χ Bχ ( 9) I od to calculat th xssios o χ B, χ B ad χ B w stat o Eq. (7), o th aticula cas o sil lcto i th io subjctd to th atic ild B (Io od). I this cas, w ust substitut () l by io ( ) μ ( io) σ io πε l V π ( 6) ( 7) ; by ( is th lctos adius), S ( ) by SSA ρ V ( SSA is th sciic suac aa o lctos i this cas: SSA A A ρ V π ρ V ), S by by S π, ξ by φ ad. Th sult is i () l 5.56π ioe χ B + μ c λ Elctodyaics tlls us that E vb c B, ad Eq. (9) s s ( ) s ( io ) ( ) ivs λ λod ( π μioσ io. Substitutio o ths xssios ito Eq. () yilds ) 5.56π Bs χb + ( ) μ c Siilaly, i th cas o oto ad uto w ca wit that 5.56 π Bs χ B + ( ) μ c 5.56 π Bs χb + μ c Th adius o lcto is 6.87 (S Adix A) ad th adius o otos 5 isid th atos (ucli) is., 7 ( ), th w obtai o Eqs. () () ad () th ollowi xssios: B χ s B 9 B χ +.5 s B χ B Th, o Eq. () it ollows that χ χ B B ( ) ( 5) ( 6) Substitutio o Eqs. () ad (5) ito Eq. (6) ivs B s Bs +.5 Fo μhz, w t 6 { [ Bs ] } 7 { [ +.5 Bs } 666. whc w obtai B s.5 T Cosqutly, Eq. () ad (5) yilds χ B 666. ad ( 7) ( 8) ( 9) ( 5)

8 ( 5) χ B χ B.999 I od to th ocs F ad F hav cotay dictio (such as occus i th cas, i which th atu o th lctootiv oc is lctical) w ust hav χ B < ad χ B χ B > (S quatios (8) (9) ad ()), i.., B s < ( 5) ad 9 B +.5 s > This as that w ust hav.6 < Bs < 5.86 I th cas o ( 5) ( 5) 6 μhz Hz th sult is ( 55) T < B < s.5t Not th cylidical oat (tu, 5 ) o th iducto (Fis. ad 6). By usi oly tu it is ossibl to liiat th caacitiv ct btw th tus. This is hihly lvat i this cas bcaus th xtly-low qucy μhz would stoly icas th caacitiv actac ( X C ) associatd to th iducto. Wh a cut i asss thouh this iducto, th valu o B isid th Io od is iv by B μ μi x B wh x B is iducto s lth ad μ (vy u Io). Howv, th ctiv ability is did as μ ( ) μ + ( μ ) N, wh N is th ava datizi acto [ ]. Sic th io od has 5 diat ad hiht, th w obtai th acto γ /5 which ivs N. (S tabl V[]). Tho, w obtai μ ( ) 9.. Thus, o B s. 5T (S Eq. (9)),i.., B μ ( ) μ i xb. 5T, th valu o i ust b i A. Th, th sisto i Fi.. ust hav V A 5Ω. Th dissiatd ow is 8W. Lt us ow calculat th cut dsity thouh th Io od (Fi. ). Accodi to Eq. (9) w hav j σ io χ B M 9 χ s 7 Sic σ. S, χ 6. 8, io / χ 666., M s. k ad B 9, w obtai iv that j S α 6.6 A/ πα 5 5. isouc js α Th sistac o th Io od is x B R souc.9 Ω σ ios α A 8 w t Thus, th dissiatd ow by th Io od is P R i.66 W ( 56) d souc souc Not that this avitatioal EMF souc is a Cut Souc. As w kow, a Cut Souc is a dvic that ks ivaiabl th lctic cut btw its tials. So, i th souc is coctd to a xtal load, ad th sistac o th load vais, th th ow souc will icas o dcas its outut volta i od to aitai ivaiabl th valu o th cut i th cicuit. V souc ~ i souc R souc V Fi. Cut Souc R Load Basd o Kichho s laws w ca xss th lctic volta btw th tials o th Cut Souc, V s, by as o th ollowi latio (S Fi.): Vsouc Rsouc isouc + V wh V is th volta alid o th cha. Th taso T coctd to avitatioal EMF Souc (S Fi. ) is

9 dsid * to ak th volta V.kV@ 6Hz. Sic R i V, th w ca wit that V souc V. Thus, i th iay cicuit, th volta is V V V. kv ad th cut is i souc isouc is N N s souc souc<< A; th widi tus atio ; thus, i th scoday cicuit th outut volta is V s 6Hz ad th cut is i s 586A. Cosqutly, th souc outut ow is P Vsis 8. 9kW Not that, i od to iitializi th avitatioal EMF Souc, is usd a xtal souc, which is ovd at th iitializatio o th avitatioal EMF Souc. Now it will b show that this avitatioal EMF souc ca b iiatuizd. W stat aki x B ad ξ.5; α, d A 8, d D 6 ad. 5 (S Fi. 5). Th sh with diat is ow o Tust cabid (W+Cobalt) with 5,6k / dsity. Th M 5 6 s 6.5 k ad Sα.. Thus, o μhz Eq.() ivs χ [ +.8E ( A ) ] { } ( 57) s Fo V A ( s ) 6V ad d A 8 w t E( A ) s.5v /, ad Eq. (57) yilds χ 6.6 Fo V D ( s ) 6V ad d D 6 w t E.65V ad. ( D ) s / * Th idacs a sctivly, Z π L π μ μ N A l. 6 Sic σ 7. S io / 9 ad χ 666., th th valu o is B ad j M 9 σ io χ Bχ A/ isouc js. 66 α Th sistac o th io od is iv by x B R souc. Ω σ ios α Thus, th dissiatd ow by th Io od is Pd Rsoucisouc. 9W I th cas o th iiatuizd souc, th io od has diat ad hiht, th w obtai th acto γ / 5 which ivs N.6(S tabl V[]). Tho, w obtai μ ( ) Sic Vs VA( s) VD( s) 6V ad th sistac o th sisto R is.6ω / W (S Fi.5), th th cut o th ist souc is i. A. Thus, w t B μ ( ) μ i xb. 5T. Sic th cut thouh th scod souc is i souc. 66A, ad, i th volta quid by th cha, is V. 7V (usual lithiu battis volta), th th souc volta is iv by Vsouc Rsouc isouc + V. 7V Cosqutly, th iiatuizd souc ca ovid th ow: P V souc isoc.7v.66 A 6. This is th aitud o th ow o lithiu battis usd i obils. Not that th iiatuizd souc o avitatioal EMF dos ot d to b chad ad it occuis a volu (8 x 7 x 8. S Fi.6) siila to th volu o th obil battis. I additio, ot that th disios o this iiatuizd souc ca b uth ducd (ossibly dow to a w illits o lss). χ. d ( ) W ( ) Ω πls π ( μ μ N s As ls ) 6.5 Ω ( total) Z + Z lctd Z + ( N N s ) Z s 7. 56Ω Z s Z wh μ 6 (io cast), N, N s, l ls. 8, φ 7. 6, φ s 6. 8, A.9, A s.7. A s j

10 Mtallic i (.5 thickss) d A 8 d D 6 α d A 8 d D 6 α.7v DC 6.W ξ.5 Dilctic tub ε Tust cabid sh ( diat) Lad sh ( diat) E A(s) at K E D(s) 6V μhz.5 D 7 8 M E D 7 8 M Full wav ctii Io od ( diat, hiht) 6V μhz A 8 9 A 8 9 V.7V i s.66a R Pitd cicuit boad Cylidical Iducto tu (i adius: ).6Ω / W x B 6V μhz B.5 T D V s 6V i. A R B.5 T D V s V.7V 8 ~ 6V μhz Iitializatio souc 7 Fi. 5 A Miiatuizd Souc o avitatioal EMF

11 Io od (8 diat, hiht) B Aluiu Iducto tu (i adius: R5) 8.87kV/6Hz 7.87kV/6Hz.kV/6Hz 8 8 Coss-sctio μ μ i B.5T i A; 5 μ 9. 5Ω 8W V μhz Tasos ad Covt (6Hz/μHz) (isid) V 6Hz 8.9 kw Iitializatio souc Hih-ow Souc μ μ i B.5T i.a; μ 6.6 6V μhz 6V μhz Coss-sctio.7V DC 6.W 6 Iitializatio souc 8 Full wav ctii R 7 8 thickss Low-ow Souc Fi. 6 Schatic Diaa i D o th avitatioal EMF Soucs

12 Adix A: Th otical Radii o Elcto ad Poto It is kow that th qucy o oscillatio o a sil si oscillato is π K ( A) wh is th itial ass attachd to th si ad K is th si costat (i N ). I this cas, th stoi oc xtd by th si is lia ad iv by F Kx ( A) wh x is th dislact o th quilibiu ositio. Now, cosid th avitatioal oc: Fo xal, abov th suac o th Eath, th oc ollows th ailia Nwtoia uctio, i.., F M, wh M th ass o Eath is, is th avitatioal ass o a aticl ad is th distac btw th cts. Blow Eath s suac th oc is lia ad iv by M F ( A ) R wh R is th adius o Eath. By coai (A) with (A) w obtai K K M A χ R x Maki x R ito (A) ivs, ad substituti (A) π M R χ ( ) ( A5 ) I th cas o a lcto ad a osito, w substitut M by, χ by χ ad by R R, wh R is th adius o lcto (o osito). Thus, Eq. (A5) bcos π χ R ( A6) Th valu o χ vais with th dsity o y []. Wh th lcto ad th osito a distat o ach oth ad th local dsity o y is sall, th valu o χ bcos vy clos to. Howv, wh th lcto ad th osito a tati o aoth, th y dsitis i ach aticl bco vy sto du to th oxiity o thi lctical chas ad, cosqutly, th valu o χ stoly icass. I od to calculat th valu o χ ud ths coditios ( x R ), w stat o th xssio o colatio btw lctic cha q ad avitatioal ass, obtaid i a vious wok [ ]: q πε A7 ( iaiay ) i ( ) wh (iaiay ) is th iaiay avitatioal ass, ad i. q I th cas o lcto, Eq. (A7) ivs πε πε πε πε ( iaiay) i ( χ ) ( χ ( ) ) i al i 9 ( χi al ).6 C ( A8 ) wh w obtai i ( iaiay) i ( ) χ.8 ( A9) This is tho, th valu o χ icasd by th sto dsity o y oducd by th lctical chas o th two aticls, ud viously tiod coditios.

13 yilds iv that π χ i, Eq. (A6) χ i R Fo Quatu Mchaics, w kow that h ( A) ( ) ic A wh h is th Plack s costat. Thus, i th cas o w t i i ic h ( A) By coai (A) ad (A) w coclud that Thus, th sult is χ h 7 R.7 ( A7) i c π Not that ths adii, iv by Equatios ( A ) ad ( A7), a th adii o lctos ad otos (wh th aticl ad atiaticl (i isolatio) tat thslvs utually). Isid th atos (ucli) th adius o otos is wll-kow. Fo xal, otos, as th hydo ucli, hav a adius iv by R. 5 [, 5]. Th sto icas i sct to th valu iv by Eq. (A7) is du to th itactio with th lcto o th ato. i h c π χ i R ( A) Isolati th adius R, w t: R i χh π c 6.87 ( A) Coa this valu with th Coto sizd lcto, which dicts R.86 ad also with stadadizd sult ctly obtaid o R 7 [ ]. I th cas o oto, w hav q πε πε πε πε ( ) i ( χ ) i ( χ ( ) ) i al i 9 ( χ i al ).6 C ( A5) iaiay ( iaiay) i ( ) wh w obtai χ ( A6)

14 Adix B: A Exital Stu o Tsti a CC with Nuclus Diital Foc au ± N;. N ( ) Dilctic tub (Acylic) χ Acylic lats 5 CC χ Mtallic is 5 Rctaula lat φ 8 d ~ Vax 8 6Hz Dilctic tub Mtallic i Mtallic lat 8 d To viw χ + 6 S S φ σ E ( ai) ai α ai ( ) 6πμ ρ c [ +.65 E( A) s ] { } 5 { [ V( A) s ] } ( ) ai A s Fo V( A ) s 8kV w obtai χ 6. 8, M χ M i P M χ M i ( M i is th itial ass)

15 5 DETAILS OF PARTS 5 5 Mtal 5 Mtal 8 Acylic 5 Mtal

16 DETAIS OF THE BOX 6 6 Acylic lats x 6 x lats x x lats x x (i lats) lats x 5 x Aluiu lats x HV ds 5 6

17 7 Rcs [] D Aquio, F. () Mathatical Foudatios o th Rlativistic Thoy o Quatu avity, Paciic Joual o Scic ad Tcholoy, (),. 7-. [] Valku, V., (99) Basic Elcticity, Pot Publicatios, -8. [] Fisch-Cis, A., () Th lctoics coaio. CRC Pss,., ISBN [] D Aquio, F. (8) Pocss ad Dvic o Cotolli th Locally th avitatioal Mass ad th avity Acclatio, BR Patt Nub: PI856-5, July, 8. [5] D Aquio, F. () avity Cotol by as o Elctoatic Fild thouh as at Ulta-Low Pssu, Paciic Joual o Scic ad Tcholoy, () Novb,.78-7, Physics/79. [6] Quvdo, C. P. (977) Eltoatiso, Mcaw- Hill,. 7. [7] Halliday, D. ad Rsick, R. (968) Physics, J. Willy & Sos, Potuus Vsio, Ed. USP,.. [8] Chals, J.A., (967) Atoshic Elcticity, Pao ss, Oxod, Lodo; Kasali, N. t al., () Advacd Pollutio, chat, DOI:.577/76, ditd by Fahad Njadkooki, Publish: ITch, ISBN , ud CC BY-NC- SA. lics. [9] Kudu, J. t al., (7) Sicoducto Physics, Quatu Elctoics& Otolctoics,,,.-. [] Aloso, M. ad Fi, E. (967) Fudatal Uivsity Physics, Addiso-Wsly Co., Potuus vsio Ed Edad Blüch (97),. 5. [] Mashall, S. V. ad Skitc,.. (98 ) Elctoatic Cocts ad Alicatios, Ptic-Hall, NJ, Scod Editio,.87 [] Ch, D. t al., (99) Datizi Factos o Cylids, IEE Tasactios o Matics, Vol. 7, Nub,,. 6. Tabl V,. 6. [] Mac o. M. H., (99) Th Eiatic Elcto. Bosto: Klu Acadic, 99,. -5. [] N.D. Cook (). Modls o th Atoic Nuclus (d d.). Si ISBN [5] K.S. Ka (987). Itoductoy Nucla Physics. Wily-VCH. ISBN X.

Chapter 11 Solutions ( ) 1. The wavelength of the peak is. 2. The temperature is found with. 3. The power is. 4. a) The power is

Chapter 11 Solutions ( ) 1. The wavelength of the peak is. 2. The temperature is found with. 3. The power is. 4. a) The power is Chapt Solutios. Th wavlgth of th pak is pic 3.898 K T 3.898 K 373K 885 This cospods to ifad adiatio.. Th tpatu is foud with 3.898 K pic T 3 9.898 K 50 T T 5773K 3. Th pow is 4 4 ( 0 ) P σ A T T ( ) ( )