ma100_note24

ma100_note24 - {5-16 AfFaCa/fiém of Em 14::...

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Unformatted text preview: {5-16 AfFaCa/fiém of Em 14:: r‘iil'gfljfiz Fix/“4c I4 94%} Vécrzfor“ flags By Ccuiumb's law the aim:er- stazic fink: mailing item a single pusitiire :harm is an inversesquam field in which F is the repuisi-ie farce an a small unit positive charge. TILE velociqr vector; u.‘ the I flUld partitles are iangent The elecrrusuatic field F :I-Iar ti: Ehe Streamlines. iasults fram l'W-C- ch ages of equai aim ngth but nppaslte pulariflr. mofim'ofc 21:? Iris—I962, w! fimi’ Pa Era/:7 p151 rafbgfl. vim 5am. EL. . u 5:in kSM-lyéafii. ME 65150021222: WT? Vlflrmfijf waft)!" E NC lama/L {semi (if asmfimfifn orimfiafiaén of W 51m La _, —-.-.r O“: F? = Xiuig’) c' 1/{1gwd' +£iMJVJb if; I” ~ X ‘3'? [Degr'fi/Mefl‘ m J ardmfiafm . 3% 3V _ Si N xi § 5, ll {Gr-5:2]. /?1t_1"fl77?bresst‘éé_ —'> Wflfanf MEL-2% , Rafi fit€_ _ —r> WK,ng r‘npé’jbmafim‘fi 55f fluid can flow through it freely in either directiuta. Find the passes through the SUIEEEI: per unit 01' time, Whure tht: volume that passus through the surf-ha: in L11: that passas Ehmugh thx: surface in has negative. dire with we afar“ fing nut volume hf fluid III that the net volume is interpreted to mean positive direcliun minus the vulmne ration. LS Wu: 1‘? lit/é? v.9 in me am 55596,? M 3msz r M W15 firm _ Takitj 21—3 at: Aimi- I2 —'.'.‘I- i): #91 Zn FIE?) Figure 15.5.3 I. n kw ff; 2.?) ~7thrxi/fizfjdq3k +95 -— :JT Frxrytzj-Fffxqtz} J5 Er" 7—0—64 féfi’fi alarms: I?“ as a, ffifllfiéfi that?“er (Ff A, bx. F: :6; ; flE-EM f2, g/oam 7r£+f+zz=af r3 Osfifiwmlpf- ammie LE}, , Ornimfilfifih 49f mn/Dammifi; smifnoas _-, __} r:M,-flj+jmmg -—:»~ Z=jrfi,v’) =jrm/V) I“ = V2741er wf'ar- M; '—’ fifirflfi) fiL—jrmmfl "I" E@'+V&7 —” x:jrfflz’) I u = _ 5'1: 6:: _ n = 3.1.- a: | / fiif+£fl m I far-y?- Ev 2?? I _ r1: Ely l '5; Pailtl'u'c Fnsltrvc c-n'nntatr'un Positive Positive nrifintatinn Positive Positlw nrientarim k-cump-onent Rampant-n: l-cnrnpunent I ‘ r —_.=- _ M) V; > = <5 Negative k~cnn1 pan Ent \fll: h§i+§—;j—k / $Ifij+ggk I |< l-n= —=_ Negative nrie ntatic-n c lily {tn a r Negative nrifintaticn Negative d'J' 5'2 j-cnm tn: aent Negatiwa nrientatinn Negative I~cnmpnnent dune, rewn‘te. the equations of the surfaces :13 z “Eff-3‘} = D, :r' — gtztxil =41. Each [If Tires: equations has. Tilt: form Gt}. 3-. z) = [1 surface of n fitnctiun Gilt. y. zjl. Since me x—Efy.z}=fl and hence can be viewed 33 a level adicnt cF__G is normal to the Icyct surfncgIL 1T follows that the um: normal I] 15 etthcr ‘VGEII‘VGH or -VGH.IVG||. Hnwwcr, Lf sz. 3r. E] = z—glix. 1"}. than VG has ak—cnmponentofl; ifG[.r, y, g]- : _5-—g{zl,1;}|_than vi} has aj-cnmpunent of l; and if GU. y. z} = J: — gt}, a}. then VG has an i—cnmpnncnt cf 1. Thus. it is evident frnm Table 1513.1 EhflE in all Lhrec cascs we have VG n = . t9} II‘G’GIJ Morccvvan We Icavc has an excrcise In Show that ifflte surfaccs z = gfix. y}. 3: = gfz, x}. and x = at}: a} an: cxpreascd in vactcr forms (6}. {3"}, and {R}. than (1'5) Homing 'urcrsicrn of Theorem IEFJEJ'. fur nonparametric sufiaccs. 16.6.3 THEOREM. Let U Eve :1 snznnth a‘tarj'nca: afthefann z = gfx, 3.51. _1.' = flax}. or .r = glfy. a). and .mpppse that than rampanentflncnom of the vucwrfiefa' F RTE continuum- an an Suppose aim that the aqzmtipnfar cr L's Written as Glfx. 3'. z} = U 513' taking 3 m the In}? aide ofthc aquarium and in: R be the pmjncripn mfg an the caprdr'nma pinup darn-mined £er the independent variabln: of g. {f or has positive an'nnrarian. then In. fin? +_§.ZE —— + _j(Z;X} / TEX (2?: _%3X E} 17:71:); v—- t—rTy'd '2 EX Z=f— XL“): is GNMWF I , “néug :; we :38. VQ = tg—J—g‘, I > mmé um, fawn f afoiz? R, J wise/2e fi=Z~fi—X/:f) 1767 = 2x Fifi-2]: + E" mfF Eds : é F V671 5104 r? :5 .2,=x—2’272 144.4% ‘3? kg: WM: #241; Pt} PXR/m LEI-xi]; —a-L =1fo (X2+ja+f) M ;=;_ 9672,30 mfg; _ fist? fro (£12 m‘vzéfimfifi (xfijljhflgf/I = [gawk/a! (Fa—r I) rofrd'z? ...
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ma100_note24 - {5-16 AfFaCa/fiém of Em 14::...

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