Electromagnetismo UTP 2019
January 29, 2023 | Author: Anonymous | Category: N/A
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Ifgudtfn nc Amhcmacråf nc Wastcefs y Cdcgtr÷magf
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CDCG^RLEFHMC^AWEL
[CRALNL 2;61
[RCWCM^FNL [LR:
JLWC CNSFRNL ^LRRCW Glrlmcd C[ ( R ) YCHF Napdlefnl cm Gacmgaf y ^cgmldlhåf Amhcmacrl Cdcgtr÷magl GA[ Efcstrl cm Fneamastrfga÷m [FNC-CWFM cm Dlhåstagf Napdlefnl cm Wchuranfn y Wfdun Lgupfgalmfd Nlgcmtc Smavcrsatfral f mavcd prc hrfnl y plst hrfnl Glmsudtlråf y Fscslråf cm cd Nascöl, Aepdfmtfga÷m y Glmtrld nc Wcrvagals nc ^cdcgleumagfgal ^cdcgleumagfgalmcs mcs y ^cdceætagf Cstunals ^c÷ragls nc Rfnafgalmcs Ml Almazfmtcs Glmsudtlråf cm ^cefs nc Wchuranfn Amtchrfd CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
ISMNFECM^LW ^C×RAGLW NC DLW GFE[LW CDCG^RLEFHMÁ^AGLW F[DAGFNLW F DF CDÁG^RAGF
WSEFRAL 6. 2. 7.
WAW^ WAW^CEF CEFWW NC GL GLLRN LRNCMF CMFNFW NFW G GFR^ FR^CWA CWAFMF FMFW, W, [L [LDFR DFRCW, CW, G GADÅ ADÅMNRA MNRAGFW GFW Q CWIÁRAGFW. YCG^LRCW, IFWL WLRC RCWW RCY RCYAWA AWA×M ×M N NCC NCR NCRAYF AYFGA× GA×M M C AM AM^CH ^CHRFG RFGA×M A×M NC IS ISMGA MGALMC LMCWW CM R R2 2 Q R7
BABDALHRFIAF • • • •
Oatcd, G`frdcs: Amrlnugga÷m f df Iåsagf ncd Csfnl W÷danl, Rcvcrá W.F., Bfrgcdlmf. 6119. Yarhadal Glwfm, Gdync D Hrf`fe, B, J.: Gursl nc Iåsagf Elncrmf, @crdf, Eáxagl. 6101. Fdlmsl, Efrgcdl Iamm, Cnwfrn: Iåsgf Yld AAA Ecgæmagf Guæmgf. 6109. Fsef, @uebcrl: Amrlnugga÷m nc Iåsagf ncd Csfnl W÷danl, SMA, Daef. 611>
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CD [RLNSG^L YCG^LRAFD L [RLNSG^L GRSZ
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
[RLNSG^L NC SM CWGFDFR [LR SM YCG^LR
g CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
[RLNSG^L CWGFDFR L [RLNSG^L [SM^L
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
f
p
gls
p f
p f gls
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
L[CRFGALMCW YCG^LRAFDCW CM ^CREAMLW NC WSW GLE[LMCM^CW GFR^CWAFMFW
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
ÆDHCBRF YCG^LRAFD [RL[ACNFNCW NCD [RLNSG^L YCG^LRAFD NC YCG^LRCW
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Wa nls vcgtlrcs slm pfrfdcdls
[rlnugtl vcgtlrafd nc nls vcgtlrcs
^rapdc prlnugtl csgfdfr
^rapdc prlnugtl vcgtlrafd
Cd rcsudtfnl cs um vcgtlr. [rcgfuga÷m: Cd rcsudtfnl cs um vcgtlr Guepdc df i÷reudf nc Dfhrfmhc
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
[rlnugtl eaxtl nc vcgtlrcs
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Eudtapdagfga÷m nc n c prlnugtls csgfdfrcs y vcgtlrafdcs
Ncravfnf nc um vcgtlr
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWVSCEF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Gleplmcmtcs nc df ncravfnf nc um vcgtlr Df ncravfnf pucnc glmtcepdfrsc glel umf naicrcmgaf nc vcgtlrcs. Dfs gleplmcmtcs nc umf naicrcmgaf nc vcgtlrcs cs ahufd f df naicrcmgaf nc dfs gleplmcmtcs
Amtchrfd nc um vcgtlr quc ncpcmnc nc umf vfrafbdc csgfdfr
Cd rcsudtfnl cs um vcgtlr
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Df amtchrfd nc dåmcf
Gfsl scmgaddl: cd gfepl vcgtlrafd cs glmstfmtc, cd gfeaml cm cd quc `fy quc amtchrfr cs umf dåmcf rcgtf
Rcsudtfnl: df nastfmgaf f dl dfrhl nc df dåmcf eudtapdagfnf plr df gleplmcmtc nc df iucrzf cm csf narcgga÷m CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Gfsl hcmcrfd
ncsgleplmcr df amtchrfd navacmnl df trfycgtlraf W cmtrc cmtrc f y z pcqucöls pcqucöls irfhecmtls Df amtchrfd f dl dfrhl nc W cs cs df suef nc dfs amtchrfdcs f dl dfrhl nc gfnf uml nc dls irfhecmtls Cm gfnf uml nc dls pcqucöls irfhecmtls, df iucrzf pucnc glmsancrfrsc glel g lel glmstfmtc Cd rcsudtfnl cs um csgfdfr
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Amtchrfd nc supcriagac nc um gfepl vcgtlrafd: cd idujl
Wcf
umf iumga÷m vcgtlrafd quc ncpcmnc nc df plsaga÷m
Wcf um vcgtlr umatfral pcrpcmnagudfr f umf supcriagac. [lr glmvcmal, cd vcgtlr mlrefd umatfral nc umf supcriagac gcrrfnf sc tlef fpumtfmnl `fgaf iucrf, cm df narcgga÷m lpucstf ncd vlduecm cmgcrrfnl plr df supcriagac
Wc nciamc df amtchrfd nc idujl glel Cd rcsudtfnl cs um csgfdfr CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
IFWLRCW • Ycgtlrcs nc rltfga÷m l ifslrcs. Cd ncspdfzfeacmtl ncspdfzfeacmtl nc nc nc umf pfrtågudf quc sc eucvc glm um EFW EFW sc sc sc pucnc glmsancrfr glel df gleplmcmtc P P nc nc um vcgtlr nc dlmhatun L[‑5 F? cstc vcgtlr rltf cm scmtanl glmtrfral f dfs fhujfs ncd rcdlj fdrcncnlr nc L glm glm vcdlganfn fmhudfr yy cm gfnf amstfmtc ilref um æmhudl ) glm (t+ glm cd cjc P. Q
[frf t = ;
[‑ [‑
F ;
Y‑
F
[ P
x F gls ;
L
[‑ [ P
L x F gls t ;
t
F
t
t+;
[ x F gls t L
t+ ;
P
;
Q F
[‑ /2
v
L
x L[ F gls t ;
F t+ ;
f
Q
Q
[frf t 5 ;
x
v Fscm t
P
F gls t ; 2 f 2 F gls t 2 F gls t ;
2 F
F‑ CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Smf iumga÷m samuslanfd ncd tacepl nc umf ircgucmgaf nctcreamfnf sc gfrfgtcrazf úmagfecmtc glm nls pfræectrls, su fepdatun y su æmhudl nc ifsc. Df rcprcscmtfga÷m glepdcjf nc nag`f iumga÷m (nc umf ircgucmgaf nctcreamfnf) sc gfrfgtcrazf tfebaám glm csls nls easels pfræectrls. I÷reudf nc Cudcr
j
c gls j scm
j ( t ) Df iumga÷m Y e gls t sc pucnc rcprcscmtfr glel Rc Y e c
Cd ifslr cs umf rcprcscmtfga÷m fbrcvafnf cm df quc, vcz cstfbdcganf df ircgucmgaf, sc glepdcjf leatc ástf rcprcscmtfmnl df umf iumga÷m samuslanfd plr cd YFDLR CIAGFZ nc df easef y su ÆMHSDL Æ MHSDL NC IFWC: ILREF [LDFR
Y /
ILREF GLE[DCJF
Y c j
YFDLR CIAGFZ CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Dls ifslrcsfmhudfr pucncm glel vcgtlrcs rltftlrals ircgucmgaf cm scmtanl glmtrfral f dfs fhujfs ncd rcdlj.quc harfm glm amtcrprctfrsc Ae
Ae
Y 6
Y 2
Y 6
t f
Y 2
t b Rc
Rc
Df rcdfga÷m nc ifscs cmtrc cddls pcrefmcgc amvfrafbdc CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Y c
Y e gls( t ) Y e 6; ;
j
6;
6; c j ;
2 / ;º
2 6;
Y e 6; / 2
3
Y c j 6; c j / 2 6; j 2 2
;
Ae -3
6; 2 / ; º
-6; ;
2
>
9
Ifslrcs rcprcscmtfnls cm t 5 5 ;
0
Rc
6; 2 / 1;º CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
L[CRFGALMCW GLM IFWLRCW WLM YÆDANFW DFW EAWEFW L[CRFGALMCW NCIAMANFW CM CD ÆDHCBRF NC MÚECRLW GLE[DCJLW Ae
Eudtapdagfr Z plr plr j cquavfdc f FNCDFM^FR /2 su ifsc
j Z Z c j / 2
Navanar Z cmtrc cmtrc j cquavfdc f RC^RFWFR /2 su ifsc
Z Z c j
Rc Ae
Eudtapdagfga÷m: eudtapdagfr e÷nudls, suefr ifscs Navasa÷m: navanar e÷nudls, rcstfr ifscs
Z 6
Z 6 Z 2
Z 2
2
2 Rc
2
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Ncravfga÷m nc iumgalmcs samuslanfdcs
v(t ) gls t
v (t )
scm t gls t 2 nt
nv(t )
6,;
;,3
;,;
;
2
>
9
0
6;
62
6>
t t
Ncravfr v (t ) cquavfdc f ESD^A[DAGFR plr cd ifslr Y yy FNCDFM^FR /2
-;,3
-6,;
(Rcprcscmtfga÷m suplmacmnl plr saepdaganfn hræiagf 56. Smanfncs 56. frbatrfrafs)
su ifsc
Ae j j Y Y
Y
Rc
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
GFE[LW CWGFDFRCW Q YCG^LRAFDCW
EFHMA^SN CWGFDFR: CWGFDFR: GSFDVSACR EFHMA^SN EF^CEÆ^AGF L IÅWAGF VSC WC [SCNF RC[RCWCM^FR WLDFECM^C [LR ^CE[CRF^SRF, C^G.SM MÚECRL RCFD. CJCE[DLW: DLMHA^SN, ÆRCF, YLDSECM, EFHMA^SN YCG^LRAFD: YCG^LRAFD: WLM FVSCDDFW CM^ANFNCW CM DFW VSC FNCEÆW NCD MÚECRL VSC DFW NC^CREAMF, WC RCVSACRC C^G. GLMLGCR DFEF^CEÆ^AGL NARCGGA×M. VSC CJCE[DLW: NCW[DFZFEACM^L, ISCRZF, FGCDCRFGA×M, CD CM^C RC[RCWCM^F F CW^FW EFHMA^SNCW WC DDFEF YCG^LR .
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
GFE[L CW DF FWAHMFGA×M F GFNF [SM^L NCD CW[FGAL, GLEL BFWC L WL[LR^C NC SMF EFHMA^SN, NCD YFDLR NC SMF ISMGA×M SMÅYLGF NC [SM^L.
GFE[L CWGFDFR
CW SMF ISMGALM RCFD NC YFRAFW YFRAFBDCW CM DF VSC F GFNF [SM^L NC WS NLEAMAL WC DC FWAHMF CD YFDLR VSC ^LEF SMF NC^CREAMFNF
EFHMA^SN CWGFDFR WLBRC NAG@L [SM^L. RC[RCWCM^F DF NAW^RABSGA×M CW[FGAFD NC SMF EFHMA^SN CWGFDFR CWGFDFR,, FWLGAFMNL SM YFDLR F GFNF [SM^L NCD CW[FGAL.
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Cjcepdl nc Gfepl csgfdfr Yfdlr nc df prcsa÷m ftelsiáragf cm um `urfgæm
p p( x, y , z ) CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
GFE[L YCG^LRAFD
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Cjcepdl nc Gfepl vcgtlrafd. Ycdlganfn ncd vacmtl cm um `urfgæm
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
NCRAYFNFW [FRGAFDCW NC SM GFE[L CWGFDFR : N R 7 R Wc nciamc df ncravfnf pfrgafd nc rcspcgtl f x, glel
x, y, z
dae
x `, y, z x, y , z
`;
x ` Cs ncgar, cs glel df ncravfnf "mlrefd" tlefmnl f dfs vfrafbdcs amncpcmnacmt amncpcmnacmtcs cs y y z glel glmstfmtcs CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
: R 7 R x, y, z x x, y, z y
x, y, z x y z 6 6
x, y, z 6 z
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
: R7
R
x, y, z
xy sam x y 2 z cxp z
x, y, z y sam x xy gls x x x, y, z x sam x 2 yz y x, y, z 2 y cxp z z
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
DF NCRAYFNF NC DFW ISMGALMCW YCG^LRAFDCW NC SMF YFRAFBDC RCFD
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
NCRAYFNFW NC LRNCM WS[CRALR
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
GÆDGSDL NC DFW AM^CHRFDCW NLBDCW AM^CHRFDCW A^CRFNFW. 6.Wa N 5 _ f , bU x _ g , n U um rcgæmhudl slbrc cd gufd df iumga÷m i cs glmmuf efmcmacmnl jf ddff vvfrafbdc frafbdc x , df iumga÷m ncpcmnc nc y, c amchrfmnl glm rcspcgl f y , sc cmc cmc
ddfefnf amtchrfd atcrfnf nc i Fnceæs 5
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Q
P
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
AM^CHRFD ^RA[DC
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
RCHALMCW NC AM^CHRFGA×M
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Q5i(x,z) P5 i(y,z)
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Cjcepdl 6
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
y
y
x
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
Cjcepdl 2 Nctcreamfr cd s÷danl guyl vlduec vlduecm m cs nfn nfnl l plr df amtch amtchrfd rfd
CWGSCDF NC AMHCMACRÅF CDÁG^RAGF Q NC [L^CMGAF
HRFGAFW [LR WS F^CMGA×M
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