solução cap.3 reitz eletromagnetismo

18
W r= Vhswhpehu 4</ 5336 Sdjh= 4 +Fkdswhu khdg=,Fdsðwxor 6= t H{hufðflr 614= W hprv txh r srwhqfldo dvvrfldgr dr sureohpd/ gdgd d vlphwuld/ ghyh srghu vhu hvfulwr frpr ) ' o n rqgh h vær dv frqvwdqwhv d vhuhp ghwhuplqdgdv1 +d, Sdud rv srq wrv lqwhuqrv/ whprv= sdud txh dv ghwhuplqhprv/ edvwd xvdu dv frqglêøhv gh frqwruqr/ gdgdv sru ) Eo @ ' ) @ ) Eo K ' ) K sdud rewhu r vlvwhpd o@ n ' ) @ o K n ' ) K fxmdv vroxêøhv vær ' o K o @ E) @ c ) K o K c o @ h ' ) K o K c ) @ o @ o K c o @ c gh prgr txh qrvvr srwhqfldo fd ) Eo ' o K o @ E) @ c ) K o K c o @ o n ) K o K c ) @ o @ o K c o @ txh ì r uhvxowdgr ghvhmdgr1 +e, Sdud rv srq wrv h{whuqrv whprv vlpsohvphqwh +ohpeuh0vh gr hihlwr gd eolqgdjhp, ) Eo ' o K ) K o t H{hufðflr 615= Djrud d glvwulexlêær ì floðqgulfd1 D lgìld ì d phvpd gr h{hufðflr dqwhulru/ pxgdqgr dshqdv d irupd sduwlfxodu gr srwhqfldo/ txh hvfuhyhprv ) ' *? o n Dv frqglêøhv gh frq wruqr lpsolfdp txh +d, sdud srqwrv lq whuqrv= ) @ ' *? o @ n ) K ' *? o K n c gh prgr txh ' ) K c ) @ *? Eo K *o @ h ' *? Eo ) @ K *o ) K @ *? Eo K *o @ c h/ sruwdq wr/ ) Eo ' ) K c ) @ *? Eo K *o @ *? o n *? Eo ) @ K *o ) K @ *? Eo K *o @ +e, Sdud srqwrv h{whuqrv/ whuhprv/ frpr dq whulruphq wh ) Eo ' ) K *? o K *? o

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Page 1: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 4+Fkdswhu khdg=,Fdsðwxor 6=t H{hufðflr 614= Whprv txh r srwhqfldo dvvrfldgr dr sureohpd/ gdgd d vlphwuld/ ghyhsrghu vhu hvfulwr frpr ) ' �o n�rqgh � h � vær dv frqvwdqwhv d vhuhp ghwhuplqdgdv1 +d, Sdud rv srqwrv lqwhuqrv/whprv= sdud txh dv ghwhuplqhprv/ edvwd xvdu dv frqglêøhv gh frqwruqr/ gdgdv sru) Eo@� ' )@) EoK� ' )Ksdud rewhu r vlvwhpd � �o@ n� ' )@�oK n� ' )Kfxmdv vroxêøhv vær � ' oKo@ E)@ c )K�oK c o@ h � ' )KoK c )@o@oK c o@ cgh prgr txh qrvvr srwhqfldo �fd

) Eo� ' oKo@ E)@ c )K�oK c o@ �o n )KoK c )@o@oK c o@txh ì r uhvxowdgr ghvhmdgr1 +e, Sdud rv srqwrv h{whuqrv whprv vlpsohvphqwh +ohpeuh0vhgr hihlwr gd eolqgdjhp, ) Eo� ' oK)Ko �t H{hufðflr 615= Djrud d glvwulexlêær ì floðqgulfd1 D lgìld ì d phvpd gr h{hufðflrdqwhulru/ pxgdqgr dshqdv d irupd sduwlfxodu gr srwhqfldo/ txh hvfuhyhprv) ' � *? o n��Dv frqglêøhv gh frqwruqr lpsolfdp txh +d, sdud srqwrv lqwhuqrv=� )@ ' � *? o@ n�)K ' � *? oK n� cgh prgr txh � ' )K c )@*? EoK*o@� h � ' *? Eo)@K *o)K@ �*? EoK*o@� ch/ sruwdqwr/ ) Eo� ' )K c )@*? EoK*o@� *? o n *? Eo)@K *o)K@ �*? EoK*o@� �+e, Sdud srqwrv h{whuqrv/ whuhprv/ frpr dqwhulruphqwh) Eo� ' )K*? oK *? o�

Page 2: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 5t H{hufðflrv 616= Vdehprv txh )� E%c +c 5� ì xpd vroxêær gd htxdêær gh Odsodfh1 Dvvlp/whprv U2)� E%c +c 5� ' f�Ghulydqgr dperv rv odgrv gd htxdêær frp uhodêær d txdotxhu yduläyho h xp qýphurtxdotxhu gh yh}hv/ �fdprv frpY?Y%�Y%2 d d d Y%?

�Y2)�Y%2 n Y2)�Y+2 n Y2)�Y52 � ' f�Frpr srghprv lqyhuwhu dv rughqv gh ghulydêær/ �fdprv frpY2)2Y%2 n Y2)2Y+2 n Y2)2Y52 ' fcrqgh )2 ' Y?)�Y%�Y%2 d d d Y%? �t H{hufðflr 617= Vdehprv txh ) vdwlvid} d htxdêær gh Odsodfh hp wrgd d uhjlær Tf1Sdud surydu txh r ydoru gh ) hp xp srqwr txdotxhu J ì d pìgld gh vhxv ydoruhv qxpdvxshuiðflh gh txdotxhu hvihud fhqwudgd hp J txh vh vlwxd lqwhludphqwh hp Tf/ rx vhmd/

) EJ� ' �eZ-2L7 )_@csrghprv vhjxlu d vxjhvwær gr olyur h frorfdu � ' �*o qd htxdêær +408:, sdud rewhu]

T��oU2)c )U2�o� _� ' L7

� �-U)c )U �-� d ?_@�Qrwh djrud txh U2) ' f h txh U2 E�*o� ' ceZB EOo�/ gh prgr txh �fdprv frp

eZ) EJ� ' L7� �-U)c )U �-� d ?_@�

R vhjxqgr whupr iruqhfh U E�*-� ' cO-*-� h frpr ? ì udgldo/ srlv d vxshuiðflh ì xpdhvihud/ �fdprv frp U E�*-� ' O- d ?*-� ' c�*-21 Qrvvr uhvxowdgr �fdeZ) EJ� ' �-2

L7 )_@n

L7�-U) d ?_@�

Sdud surydu txh d ýowlpd lqwhjudo ì qxod/ ghyhprv qrv ohpeudu txh hvwdprv qxpduhjlær olyuh gh irqwhv gh fdujdv/ srlv d htxdêær gh Odsodfh ydoh1 Wdpeìp ghyhprv qrvohpeudu txh O. ' cU) h txh�- L7 U) d ?_@ ' c �- L7 O. d ?_@ ' c-̂0f c

Page 3: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 6frp ^ ' f1 Dvvlp/ �fdprv frp

eZ) EJ� ' �-2L7 )_@rx vhmd ) EJ� ' �eZ-2L7 )_@txh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 618= Sdud h{sdqglu d ixqêær

8 E�� ' ��c 2%+ n �2�3�*2edvwd xvdu d vìulh gh Wd|oru xvxdo=

8 E�� ' 8 Ef� n ��- Y8 E��Y� �����'f �� n �2- Y28 E��Y�2�����'f �2 n J ���� '

' � n %�n��2%2 c �2��2 n�D2%� c �2%��� n J ��e� �Vh frorfduprv hp ixqêær gh xpd vrpd h qrwduprv txh rv whuprv hp % vær rv srolq÷plrvgh Ohjhqguh/ whuhprv 8 E�� ' "[

?'f �? E%� �?cfrpr txhuðdprv ghprqvwudu1t H{hufðflr 619= Sdud ghprqvwudu txh d phwdgh grv kdup÷qlfrv }rqdlv vær jhudgrvdwudyìv gd ghulydêær vxfhvvlyd gh o3� hp uhodêær ã frrughqdgd uhwdqjxodu 5 +5 'o ULt w,/ srghprv id}hu=YY5 ��o� ' c �o2 YoY5 ' co32 ULt w ' o32�� Ew�h wdpeìpY2Y52 ��o� ' c YY5 � �o2 YoY5� ' 2o3��YoY5�2 c �o2 Y2oY52 ' 2o3� ULt2 Ew� ���

t H{hufðflr 61:= Vdehprv txh U2 ' Y2Y%2 n Y2Y+2h txh % ' o ULt w h + ' o t�? w1 Dvvlp/ whprv/ sru lqyhuvær=o 's%2 n +2 h w ' @hU|@? E+*%�

Page 4: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 7gh prgr txhYY% ' YoY% YYo n YwY% YYw ' %s%2 n +2 YYo c +%2 n +2 YYw ' ULt w YYo c t�? wo YYwYY+ ' YoY+ YYo n YwY+ YYw ' +s%2 n +2 YYo n %%2 n +2 YYw ' t�? w YYo n ULt wo YYwSdud rewhu dv ghulydgdv gh vhjxqgd rughp/ id}hprvY2Y%2 ' �ULt w YYo c t�? wo YYw��ULt w YYo c t�? wo YYw� '

' ULt2 w Y2Yo2 n ULt w t�? wo2 YYw n t�?2 wo YYo n t�?2 wo2 Y2Yw2 n ULt w t�? wo2 YYwh wdpeìpY2Y+2 ' �t�? w YYo n ULt wo YYw��t�? w YYo n ULt wo YYw� '' t�?2 w Y2Yo2 c ULt w t�? wo2 YYw n ULt2 wo Y2Yo n ULt2 wo2 Y2Yw2 c ULt w t�? wo2 YYwtxh vrpdgrv gær

U2 ' Y2Y%2 n Y2Y+2 ' � Y2Yo2 n �o YYo�n �o2 Y2Yw2 ' �o YYo �o YYo�n �o2 Y2Yw2 ctxh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 61;= Qr h{hufðflr 5155/ fdsðwxor 5/ rewlyhprv txh) Eoc wc �� ' E2^,2�eZ0fo�

��2 ULt2 w c �2�h frpr �2 Ew� ' ��2 ULt2 w c �2�/ �fd hvwdehohflgr r uhvxowdgr1t H{hufðflr 61<= Whprv xp glsror srqwxdo orfdol}dgr qr fhqwur gh xpd fdvfd hviìulfdfrqgxwrud frqhfwdgd ã whuud +srwhqfldo qxor,1 Sdud ghwhuplqdu r srwhqfldo qr lqwhulrugd fdvfd/ srghprv xvdu rv kdup÷qlfrv }rqdlv txh vær �qlwrv qd ruljhp Eo ' f�/ mätxh ghyhprv whu vroxêær ehp frpsruwdgd dð/ h{fhwr shor idwr gh whuprv xp glsrorsrqwxdo qd ruljhp h d glyhujíqfld ghyhu vhu gr wlsr dvvrfldgr d hvwd glvwulexlêær ghfdujd1 Dvvlp/ qrvvr srwhqfldo �fd gdgr sru) Eoc w� ' "[

?'f��?o? n�?o3E?n����? Ew� c

Page 5: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 8h d lgìld ì rewhu dv frqvwdqwhv �? h �? gdv frqglêøhv gh frqwruqr gr sureohpd1Hvwdv frqglêøhv gh frqwruqr srghp vhu idflophqwh gdgdv vdehqgr0vh txh sdud o pxlwrshtxhqrv/ ghyhuhprv whu r srwhqfldo sudwlfdphqwh ljxdo ãtxhoh gh xp glsror srqwxdo/mä txh ì xp glsror srqwxdo txh vh hqfrqwud qd ruljhp1 Dvvlp/ vdehqgr0vh txh rsrwhqfldo gr glsror srqwxdo ì gdgr sru

)_�R ' �eZ0f R ULt wo2 c�fd fodur txh +ohpeuh0vh txh qd ruljhp rv whuprv hp �? vh fdqfhodp, ghyhprv dqxoduwrgrv rv frh�flhqwhv �? sdud ? �' �/ mä txh gær glyhujíqfld glvwlqwd gd txh hvshudprvsdud d glvwulexlêær gh fdujd hp txhvwær1 Pdlv dlqgd/ �� ' R/ hylghqwhphqwh1 Djrud/vdehqgr0vh txh d hvihud hvwä dwhuudgd/ hqwær vdehprv txh hp o ' @ +udlr gd hvihud,/ghyhprv whu ) E@c w� ' f +txh ì d rxwud frqglêær gh frqwruqr gr sureohpd,1 Ohydqgrqd h{suhvvær sdud r ) gdgd dflpd/ whprv

) E@c w� ' "[?'f�?@?�? Ew� n �eZ0f R ULt w@2 ' f�

Qrwh txh r whupr hp ? ' f ì xp whupr frqvwdqwh h qær id} glihuhqêd qd dqäolvh ghxp srwhqfldo1 Dvvlp/ qrvvd dqäolvh �fd gdgd sru) E@c w� ' ���@n �eZ0f R@2� ULt w n "[

?'2�?@?�? Ew� ' fcrqgh mä lvrodprv r sulphlur whupr hp ULt w1 Djrud qrwh txh rv kdup÷qlfrv }rqdlv �? Ew�vær olqhduphqwh lqghshqghqwhv1 Dvvlp/ srghprv dqxodu r sulphlur whupr frorfdqgr

�� ' c �eZ0f R@� cpdv rv rxwurv whuprv vö srghuær vhu dqxodgrv vh frorfduprv �? ' f vh ? z 21 Dvvlp/qrvvr srwhqfldo �fd frpsohwdphqwh ghwhuplqdgr h ì gdgr sru) Eoc w� ' �eZ0f

��c o�@�� R ULt wo2 ctxh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 6143= Mä hqfrqwudprv r srwhqfldo gh xpd hvihud frqgxwrud qær fduuhjdgd/vlwxdgd qxp fdpsr hoìwulfr lqlfldophqwh xqliruph1 R srwhqfldo ì gdgr sru

) Eoc w� ' c��c @�o��.fo ULt w '' c.fo ULt w n .f@�o ULt wo�

Page 6: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 9R sulphlur whupr ì r whupr gh fdpsr frqvwdqwh/ hqtxdqwr txh r vhjxqgr ì gdgr sru

)W Eoc w� ' �.f@�&� d Ooo� �D frpsdudêær ghvwh whupr frp r srwhqfldo ghylgr d xp glsror srqwxdo/ gdgr sru

)_�R Eoc w� ' OR d OoeZ0fo�prvwud txh )W Eoc w� uhsuhvhqwd xp srwhqfldo gh glsror srqwxdo qd ruljhp frpprphqwrgh glsror hoìwulfr gdgr sru OR ' eZ0f@�.f&�R srwhqfldo )W Eoc w� ì r srwhqfldo ghylgr ã hvihud/ mä txh d sduwh gh fdpsr frqvwdqwhmä irl uhwludgd h qær kä rxwudv irqwhv sdud r srwhqfldo1t H{hufðflr 6144= D hvihud whp udlr @ h srvvxl xpd fdujd ' h hvwä qxp fdpsr hoìwulfrlqlfldophqwh xqliruph1 Hvwh sureohpd ì vlplodu dr txh irl uhvroylgr qr frusr gr olyur/kdyhqgr dshqdv d dowhudêær gh txh/ djrud/ d hvihud frqgxwrud srvvxl xpd fdujd oðtxlgd1D vlphwuld ì hviìulfd +ghylgr ãv frqglêøhv gh frqwruqr, h r srqwhqfldo srgh vhu hvfulwrfrpr) Eoc w� ' "[

?'f��?o? n�?o3E?n����? EULt w� '

' �f n��o ULt w n "[?'2 �?o?�? EULt w� n

n��o n �2o2 ULt w n "[?'2

�?o?n��? EULt w� �D frqglêær gh frqwruqr qr lq�qlwr gl} txh ) E�c w� ' c.fo ULt w/ gh prgr txh ghyh0prv dqxodu wrgrv rv whuprv gr wlsr o& frp & z 21 Doìp glvvr/ �� ' c.f1 Ilfdprvhqwær frp

) Eoc w� ' �f c.fo ULt w n ��o n �2o2 ULt w n "[?'2

�?o?n��? EULt w� �Qrwh djrud txh d hvihud hvwä fduuhjdgd/ gh prgr txh r whupr ��*o qær srgh vh dqxoduh/ dlqgd sru flpd/ ghyh gdu r uhvxowdgr �� ' '*eZ0f/ mä txh vreuh d vxshuiðflh gdhvihud ghyhprv whu xp srwhqfldo

) E@c w� ' 'eZ0f@�

Page 7: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= :Dvvlp/ d frqglêær gh frqwruqr vreuh d vxshuiðflh gd hvihud �fd +�f ' f,

) E@c w� ' 'eZ0f@ n��2@2 c .f@� ULt w n "[?'2

�?@?n��? EULt w� ' 'eZ0f@crx vhmd ��2@2 c .f@� ULt w n "[?'2

�?@?n��? EULt w� ' fcsdud txdotxhu w1 Frpr rv srolq÷plrv gh Ohjhqguh vær olqhduphqwh lqghshqghqwhv/ghyhprv whu txh fdgd frh�flhqwh gh �? EULt w� dflpd +lqfoxlqgr r ULt w ' �� EULt w�,ghyh dqxodu0vh1 Dvvlp/ �fdprv frp�2 ' .f@� h �? ' f vh ? z 2�R srwhqfldo �fd/ sruwdqwr/

) E@c w� ' 'eZ0fo n�.f@�o2 c.fo� ULt wtxh qdgd pdlv ì gr txh r srwhqfldo sdud xpd hvihud ghvfduuhjdgd qxp fdpsr hoìwulfrxqliruph +uhvxowdgr rewlgr qr frusr gr wh{wr, dglflrqdgd dr srwhqfldo gh xpd hvihudfduuhjdgd frp fhqwur qd ruljhp +ohpeuh0vh txh ydoh d vxshusrvlêær sdud dv vroxêøhvgd htxdêær gh Odsodfh,1t H{hufðflr 6145= Djrud whprv xp frqgxwru floðqgulfr ghvfduuhjdgr/ phwäolfr/ qd suh0vhqêd gh xp fdpsr hoìwulfr lqlfldophqwh frqvwdqwh1 R hl{r 5 ghyh vhu frorfdgr qd gl0uhêær gr hl{r gr flolqgur h r srwhqfldo qr lq�qlwr �fd gdgr sru ) E�c w� ' c.fo ULt w/frpr dqwhulruphqwh +pdv hp frrughqdgdv floðqgulfdv/ rx vhmd/ r o dtxl whp vljql�fdgrglvwlqwr gr o hp frrughqdgdv hviìulfdv/ dvvlp frpr r w,1 D frqglêær gh frqwruqr vreuhd vxshuiðflh gr flolqgur srgh vhu hvfulwd frpr ) E@c w� ' f1 R srwhqfldo ì xpd vroxêærjhudo gd htxdêær gh Odsodfh hp frrughqdgdv floðqgulfdv +rqgh whprv vlphwuld sodqdutxh qrv srvvlelolwrx holplqdu rv whuprv Y2*Y52 gr odsodfldqr, h ì gdgr sru

) Eoc w� ' �f n�f *? o n "[?'�

��?o3? n�?o?� d�? ULt E?w� n(? t�? E?w�o �R whupr hp �f ì xpd frqvwdqwh lqhvvhqfldo/ gh prgr txh �f ' f vhp shugd ghjhqhudolgdgh1 R flolqgur qær ì fduuhjdgr/ gh prgr txh �f ' f1 Doìp glvvr/ d frqglêærgh frqwruqr hp o � � lpsolfd txh �? ' f vh ? z 21 Ilfdprv/ sruwdqwr/ dwì dtxl/frp r srwhqfldo

) Eoc w� ' ���o ULt w n����o t�? w n "[?'� o3? d� �? ULt E?w� n(�? t�? E?w�o c

Page 8: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= ;rqgh mä *dvvlplodprv* d frqvwdqwh �? hp ��? h (�?1 Qrwh djrud txh d frqglêær ghfrqwruqr qr lq�qlwr qrv frpsurphwh hp frorfdu r hl{r % qd gluhêær gr fdpsr hoìwulfrfrqvwdqwh/ rx vhmd/ hvwlyhprv vxsrqgr dwì dtxl txh O. ' .f%1 Frp hvwd vlphwuld/ qærhvshudprv txh r srwhqfldo srvvd vh dowhudu txdqgr id}hprv w � cw1 Ghvwh prgr/ghyhprv holplqdu rv whuprv hp t�? w gd h{suhvvær dflpd sdud rewhu

) Eoc w� ' ���o ULt w n "[?'� � �?o3? ULt E?w� �

Dvvlp/ frp o � � �fdprv dshqdv frp r sulphlur whupr h frqfoxlprv idflophqwh txh��� ' c.f1 Djrud/ sdud d frqglêær gh frqwruqr vreuh r flolqgur/ whprv) Eoc w� ' �c.f@n � ��@ � ULt w n "[

?'2 � �?@3? ULt E?w� ' f�Frpr dv ixqêøhv ULt w vær olqhduphqwh lqghshqghqwhv/ �fdprv frp � �? ' f vh ? z 2 h� �� ' .f@21 R uhvxowdgr �qdo sdud r srwhqfldo �fd

) Eoc w� ' c.f�o c @2o � ULt w�

Dv fxuydv gh srwhqfldo �fdp frpr prvwudgr qd �jxud dedl{r +@ ' �,

D ghqvlgdgh vxshu�fldo gh fdujd �fd gdgd sruj Ew� ' c.f

�� n @2o2� ULt wR juä�fr gd glvwulexlêær gh fdujdv �fd gdgr shod �jxud d vhjxlu=

Page 9: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= <

qrwh txh/ vreuh r hl{r %/ whprv xpd glvwulexlêær gh fdujdv qhjdwlydv sdud % : f hsrvlwlydv sdud % f/ frpr hvshudgr1t H{hufðflr 6146= R srwhqfldo ì) Eoc w� ' �o�*2 t�? w2 ' W4��S5� 1Hp frrughqdgdv floðqgulfdv/ whprvY)Yo ' �2So t�? w2 h Y)Yw ' So2 ULt w2gh prgr txh Y2)Yo2 ' c �eo�*2 t�? w2 h �o2 Y2)Yw2 ' c �eo�*2 t�? w2h/ sruwdqwr/Y2)Yo2 n �o Y)Yo n �o2 Y2)Yw2 ' c �eo�*2 t�? w2 n �o �2So t�? w2 c �eo�*2 t�? w2 ' f�

Gl}0vh txh hvwh srwhqfldo srgh vhu xvdgr sdud ghvfuhyhu r sureohpd gh xp sodqrfduuhjdgr frqgxwru hp %5 +rx vhmd/ + ' f,1 Hvwh srwhqfldo ì ghvfrqwðqxr hp w ' f/srlv d ixqêær qær uhwruqd d vhxv ydoruhv gh dqwhv vh gdprv xpd yrowd frpsohwd qrsodqr w � w n 2Z1 D ixqêær dflpd/ S5 ì xpd ixqêær pxowlydorudgd h/ sdud wruqdu0vhxqlydorudgd/ ghyhprv frqvwuxlu sdud hod xpd vxshuiðflh gh Ulhpdqq gh gxdv irokdv1 Dghqvlgdgh gh fdujd vreuh r sodqr �fd gdgd sruY)Y+ ����+'f ' �2So YoY+ t�? w2 n �2So ULt w2 YwY+ '' +2o t�? w2 n %2o ULt w2 '' �2 �t�? w t�? w2 n ULt w ULt w2� ' �2 ULt�w c w2� ' �2 ULt w2 �

Page 10: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 43R juä�fr gdv fxuydv htxlsrwhqfldlv �fd

rqgh srghprv qrwdu r hqfxuydphqwr gdv htxlsrwhqfldlv/ lqglfdqgr txh r fdpsr/ shuwrgd erugd gr sodqr +uhsuhvhqwdgr shod olqkd suhwd fkhld, whqghuä d glyhujlu *sdud irud*/uhsuhvhqwdqgr rv hihlwrv gh erugd1t H{hufðflr 6147= Shor pìwrgr gdv lpdjhqv/ whprv txh r srwhqfldo �fd gdgr sru) E%c +c 5� ' ^eZ0f

57 �tE%c _�2 n +2 n 52 c �tE%n _�2 n +2 n 5268

gh prgr txh d ghqvlgdgh vxshu�fldo gh fdujd �fd gdgd sru +r sodqr hvwä hp +5,j Efc +c 5� ' c0f Y)Y% ����%'f ' c_^2Z �d_2 n +2 n 52o�*2h d fdujd wrwdo lqgx}lgd �fd

j|J|@, ' c_^2Z ] n"3"

] n"3"

�d_2 n +2 n 52o�*2_5_+ '' c_^2Z ] n"

3"2_2 n 52_5 ' c^c

frpr hvshudgr1t H{hufðflr 6148= Whprv dv fdujdv sxqwliruphv ^� h ^2 orfdol}dgdv suö{lpdv d xp sodqrfrqgxwru ghvfduuhjdgr +) ' f,1 Dv fdujdv lpdjhqv vhuær c^� h c^2 orfdol}dgdv hvshfx0oduphqwh d ^� h ^2/ uhvshfwlydphqwh1 Ì öeylr/ sruwdqwr/ txh ghyhprv vhpsuh hvfrokhu/qxpd glvwulexlêær 4 EOo� frqwðqxd/ d glvwulexlêær c4 EOo�/ hvshfxoduphqwh srvlflrqdgdfrp uhodêær dr sodqr frqgxwru1

Page 11: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 44t H{hufðflr 6149= D srvlêær grv sodqrv ì gdgd shod �jxud dedl{r/ ehp frpr d srvlêærgdv fdujdv srqwxdlv1

Dv srvlêøhv gdv fdujdv wdpeìp hvwær prvwudgdv h vær rv uh h{rv hvshfxoduhv gdvphvpdv frp uhodêær drv sodqrv1 Irupdp xp kh{djrqr/ srlv d fdujd lqlfldo +uhdo,/irupd gxdv lpdjhqv hvshfxoduhv +yhuphokdv, txh/ sru vxd yh}/ irupdp gxdv lpdjhqvhvshfxoduhv +yhughv, txh irupdp d phvpd lpdjhp hvshfxodu +d}xo,/ gdqgr r kh{djrqrgd �jxud dqwhulru1t H{hufðflr 614:= Whprv xpd vlwxdêær frpr d prvwudgd qd �jxud d vhjxlu=

Page 12: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 45h d iruêd �fd8 ' ^2eZ0f

�c �E2_c 2%�2 c �E2%�2 n �E2_�2 n �E2_�2 c �E2_n 2%�2 c �Ee_c 2%�2 n �Ee_�2 d d d � '' ^2�SZ0f_2� ��2 n 2c �E�c ��2 c �E� n ��2 c �E2c ��2 n �2�

' ^2�SZ0f_2+ ��2 n "[

?'�� 2?2 c� �E?n ��2 n �E?c ��2

��,rqgh � ' %*_1 D glihuhqêd sdud r uhvxowdgr gr olyur ghyh0vh drv srqwrv rqgh irudpfrorfdgrv rv sodqrv1t H{hufðflr 614;= Sdud hqfrqwudu d iruêd hqwuh d fdujd sxqwliruph h d hvihud fduuhjdgd/srghprv frqvlghudu r sureohpd htxlydohqwh shor pìwrgr gdv lpdjhqv/ vhjxqgr r txdokä dshqdv gxdv fdujdv sxqwliruphv1 Xpd gh ydoru ^/ vlwxdgd d xpd glvwåqfld _ gdruljhp h xpd vhjxqgd gh fdujd ^� ' c@^*_ vlwxdgd d xpd glvwåqfld K ' @2*_ gdruljhp/ rqgh @ ì r udlr gd hvihud1 Dvvlp/ d iruêd hqwuh hodv �fd gdgd sru

8^^� ' ^^�eZ0f E_c @2*_�2 ' c@^2eZ0f E_2 c @2�2 �t H{hufðflr 614<= Whprv xpd hvihud frqgxwrud qd suhvhqêd gh xp fdpsr hoìwulfrxqliruph qd gluhêær 51 Hvwh fdpsr srgh vhu uhsuhvhqwdgr shor fdpsr gh gxdv fdujdvsxqwxdlv ' h c' vlwxdgdv vreuh r hl{r 5 hp 5 ' cu h 5 ' nu/ frp u � �1 Rsrwhqfldo ghvwd frq�jxudêær ì

)e%| E%c +c 5� ' 'eZ0f57 �t%2 n +2 n E5 n u�2 c �t%2 n +2 n E5 c u�2

68 '' 'eZ0f

� �So2 n 2ou ULt w n u2 c �So2 c 2ou ULt w n u2� '

' 'eZ0fu57 �t� n 2 ou ULt w n o2u2

c �t�c 2 ou ULt w n o2u2

68 '' 'eZ0fu

���c ou ULt w c o22u2�c�� n ou ULt w c o22u2

�� '' 'eZ0fu 2o ULt wu ' '2Z0fu2 o ULt w�Gh irupd txh vh frorfduprv .f ' '*2Z0fu2/ whprv sdud u � �/ hp sulphlud rughp/txh )e%| Eoc w� ' c.fo ULt w�

Page 13: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 46Djrud whprv xpd frq�jxudêær qd txdo whprv xpd hvihud frqgxwrud qær fduuhjdgd qdsuhvhqêd gh gxdv fdujdv ' h c' gd irupd dvvlqdodgd dflpd1 Shor pìwrgr gdv lpdjhqv/srghprv ghvfrqvlghudu d hvihud h vxevwlwxð0od shodv fdujdv lpdjhqv

'� ' c @u' h '�� ' c@u Ec'� ' @'u csdud fdujdv srvlwlydv h qhjdwlydv/ uhvshfwlydphqwh/ qdv srvlêøhv

K� ' c@2u h K�� ' @2u �R sureohpd vh wruqd xp sureohpd gh txdwur fdujdv sxqwxdlv qdv srvlêøhv lqglfdgdvgh prgr txh r srwhqfldo �fd gdgr sru +r sulphlur whupr yhp gdv fdujdv qr lq�qlwr/rx vhmd/ mä �}hprv u � � qhohv/ r vhjxqgr whupr ì ghylgr ãv fdujdv qdv srvlêøhv K� hK,

) ' c.fo ULt w n c'�eZ0f57 �t%2 n +2 n E5 c K��2 c �t%2 n +2 n E5 c K���2

68 '' c.fo ULt w n c'�eZ0f

� �So2 c 2oK� ULt w n K�2 c �So2 c 2oK�� ULt w n K��2� �Qrwh djrud txh vh whprv u � �/ hqwær vær rv whuprv hp o txh vær *judqghv* frpuhodêær d K� h K�� +hvwhv ýowlprv yær sdud }hur frp u � �,1 Dvvlp/ �fdprv frp) Eoc w� ' c.fo ULt w n c'�eZ0fo

57 �t�c 2 K�o ULt w n K�2o2c �t�c 2 K��o ULt w n K��2o2

68 '' c.fo ULt w n c'�eZ0fo

��� n K�o ULt w c K�22o2�c �� n K��o ULt w c K��22o2�� '' c.fo ULt w n c'�eZ0fo�K� c K��o � ULt w ' c.fo ULt w n '2Z0fu2 @�o2 ULt w '' c.fo ULt w n.f ULt w@�o2 ' c.f

�o c @�o2� ULt wctxh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 6153= Qrwh txh djrud d fdujd hvwä qr lqwhulru gd fdvfd hviìulfd/ d qxdglvwåqfld o� gr fhqwur gd phvpd/ txh srvvxl udlr @1 Whprv txh r srwhqfldo srgh vhuhvfulwr frpr

) Eoc w� ' �eZ0f� ^So2 n o�2 c 2oo� ULt w n ^�So2 n K2 c 2oK ULt w�

Page 14: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 47rqgh ghyhprv hqfrqwudu K h ^�/ dfhuwdqgr dv frqglêøhv gh frqwruqr1 D hvihud ì frq0gxwrud/ gh prgr txh ghyhprv whu ) ' SJ?r|� ' )f1 Dvvlp/ whuhprv/ uhwludqgr dfrqvwdqwh ^So�2 n @2 c 2o�@ ULt w ' c^�S@2 n K2 c 2@K ULt wrx vhmd/ ^2 �@2 n K2 c 2@K ULt w� ' ^�2 �o�2 n @2 c 2@o� ULt w�txh ghyh ydohu sdud txdotxhu w1 Dvvlp/ ljxdodqgr rv whuprv hp w/ �fdprv frp^2K ' ^�2o�h wdpeìp ^2 �@2 n K2� ' ^�2 �o�2 n @2� �Vxevwlwxlqgr d sulphlud qd vhjxqgd/ whprv�@2^e n ^�eo�2� ' ^2^�2 �o�2 n @2�h/ sruwdqwr/ o�2 �^�2�2 c ^2 �o�2 n @2� �^�2�n @2^e ' f�Hvwd htxdêær whp gxdv udð}hv= ^� ' ^ h ^�2 ' ^2@2*o�21 D sulphlud vroxêær qær srghvhu dfhlwd1 D vhjxqgd iruqhfh ^� ' c @o� ^�Ohydqgr lvwr qd htxdêær sdud K dflpd/ �fdprv frp

^2K ' ^2@2o�2 o�gh prgr txh K ' @2o� �Dvvlp/ qrvvr srwhqfldo �fd

) Eoc w� ' )f n �eZ0f57 ^So2 n o�2 c 2oo� ULt w c @o� ^to2 n @eo�2 c 2o@2o� ULt w

68Dvvlp/ d ghqvlgdgh gh fdujd qd vxshuiðflh �fd

j Ew� ' c Y) Eoc w�Yo ����o'@ '�c@2o� n o�� ULt wd@2 n o�2 c 2@o� ULt wo�*2 ctxh ì r uhvxowdgr hvshudgr1

Page 15: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 48

Iljxuh 4=t H{hufðflr 6154= Ghyhprv frqvlghudu sulphludphqwh gxdv olqkdv gh fdujd lq�qlwdvfrp ghqvlgdghv olqhduhv gh fdujd b sdudohodv h srvlflrqdgdv hp % ' f/ sdud nb h% ' c2_ sdud cb/ frpr qd �jxud dedl{r1R srwhqfldo dvvrfldgr ã frq�jxudêær grvgrlv �rv gh ghqvlgdghv nb h cb �fd +r vlvwhpd gh frrughqdgdv hvwä vreuh d olqkd ghfdujd srvlwlyd,

) Eo� ' b2Z *?3C s%2 n +2tE%n 2_�2 n +24D

h xpd vxshuiðflh htxlsrwhqfldo ) ' )f lpsolfd txhi T�2Z)fb � ' � ' s%2 n +2tE%n 2_�2 n +2

gh prgr txh e�2_2�c�2 ' %2 c e% �2_E�c�2� n +2rx dlqgd �%c 2�2�c�2_�2 n +2 ' �2_2E�c�2�2gh irupd txh whprv xpd vxshuiðflh gh srwhqfldo qxp fðufxor frp udlr �_* E�c�2�h fhqwur hp % ' 2�2* E�c�2�/ + ' f1 Dvvlp/ whprv txh

@ ' �_�c�2

Page 16: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 49h/ shod �jxud/ %f c _ ' 2�2�c�2_�Dvvlp/ %f ' �2 n ��c�2_ ' �2 n ��c�2 E�c�2�� @rx vhmd/ %f@ ' �2 n �� �Uhvroyhqgr hvwd htxdêær hp � / �fdprv frp

�2 c %f@ � n � ' f � � ' %f2@ n 2u %2f2@2 c �txh ì r uhvxowdgr surfxudgr1t H{hufðflr 6155= D ghqvlgdgh ì gdgd sru 4 EOo� ' 4f sdud o y - h 4 EOo� ' f sdudo : -1 Sdud fdofxodu r srwhqfldo xvdqgr d htxdêær gh Srlvvrq/ edvwd qrwdu txh hvwdhtxdêær �fd gdgd sru U2) Eoc wc �� ' c4 EOo�0f �Frpr d ghqvlgdgh ì ixqêær dshqdv gh o/ whprv txh�o2 __o �o2_) Eo�_o � ' c4 Eo�0f �Srghprv lqwhjudu hvwd htxdêær gluhwdphqwh sdud rewhu] o

f__o� �o�2 _)_o�� _o� ' c �0f ] o

f o�24 Eo�� _o�h/ sruwdqwr/ sdud o : -/ whprv

o2_)e%|_o ' c ��0f-�gh prgr txh ] o

f_)e%|_o� ' c-��0f ] �o�2_o�gdqgr )e%| Eo� ' -��0fo �Vh o -/ hqwær whprv o2_)�?|_o ' c ��0fo�

Page 17: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 4:gh prgr txh ] _)�?|_o� ' c ��0f ] o�_o�h )�?| Eo� ' )f c �S0f o2�Frpr hp o ' - ghyhprv whu )e%| E-� ' )�?| E-�/ srghprv hvfuhyhu-2�0f ' )f c �S0f-2cgh prgr txh )f ' -220f �Dvvlp/

)�?| Eo� ' -220f��c o2�-2

�)e%| Eo� ' -��0fo+frpsduh frp r uhvxowdgr gr h{hufðflr 2��DK,1t H{hufðflr 6156= Whprv xp glsror rulhqwdgr shushqglfxoduphqwh d xp sodqr frqgxwrulq�qlwr h d xpd glvwåqfld _ gr phvpr1 Sdud fdofxodu d iruêd h{huflgd shor glsror vreuhr sodqr/ edvwd xvdu r pìwrgr gdv lpdjhqv1 Vdehprv txh/ vh d srvlêær gdv fdujdv uhdlvvær= n^ hp 5 ' _ h c^ hp 5 ' _n ,/ hqwær dv fdujdv lpdjhp hvwduær qdv srvlêøhv= c^hp 5 ' c_ h n^ hp 5 ' c_c ,1 R srwhqfldo jhudgr shodv fdujdv uhdlv/ �fd sruwdqwr

) E%c +c 5� ' ^eZ0f57 �t%n +2 n E5 c _�2 c �t%2 n +2 n E5 c _c ,�2

68 �D iruêd h{huflgd shor glsror vreuh r sodqr ì gdgd shod iruêd txh dv fdujdv uhdlv id}hpvreuh dv fdujdv lpdjhqv/ vrpdgdv yhwruldophqwh1 Whprv iruêd dshqdv qd gluhêær 5/ sruvlphwuld/ gh prgr txh srghprv fdofxodu dshqdv 851 R fdpsr hoìwulfr .5 dvvrfldgr drsrwhqfldo dqwhulru �fd.5 E%c +c 5� ' cY)Y5 ' ^eZ0f

+ 5 c _�%n +2 n E5 c _�2��*2 c 5 c _c ,�%2 n +2 n E5 c _c ,�2��*2, �

D iruêd vreuh d fdujd lpdjhp c^ vlwxdgd hp 5 ' c_ �fdc^.5 Efc fcc_� ' ^2eZ0f

� 2_E2_�� c 2_n ,E2_n ,��� ' ^2eZ0f

� �e_2 c �E2_n ,�2�

Page 18: Solução Cap.3 Reitz Eletromagnetismo

Wr= Vhswhpehu 4</ 5336 Sdjh= 4;hqtxdqwr txh d iruêd vreuh d fdujd lpdjhp n^ vlwxdgd hp 5 ' c_c , �fd

n^.5 Efc fcc_c ,� ' ^2eZ0f�c �E2_n ,�2 n �e E_n ,�2

�h d iruêd wrwdo �fd

85 ' c^.5 Efc fcc_� n ^.5 Efc fcc_c ,� '' ^2�SZ0f_2

%�c 2�� n ,2_�2 n ��� n ,_�2& '

' ^2�SZ0f_2+�c 2%�c 2 ,2_ n �� ,2_�2&n %�c 2 ,_ n �� ,_�2&, '

' ^2�SZ0f_2�c�2 ,2_2 n � ,2_2� ' �^2,2�2Z0f_e ' �R2�2Z0f_e crx vhmd 85 ' �R2�2Z0f_etxh ì xpd iruêd gh dwudêær1t H{hufðflr 6158= Frqvlghuh dv h{sdqvøhv=

) E%n _c +c 5� ' )n _Y)Y% n �2_2 Y2)Y%2) E%c _c +c 5� ' )c _Y)Y% n �2_2 Y2)Y%2) E%c + n _c 5� ' )n _Y)Y+ n �2_2 Y2)Y+2) E%c + c _c 5� ' )c _Y)Y+ n �2_2 Y2)Y+2) E%c +c 5 n _� ' )n _Y)Y5 n �2_2 Y2)Y52) E%c +c 5 c _� ' )c _Y)Y5 n �2_2 Y2)Y52

Vrpdqgr0dv/ whprv [ ' S)n _2 �Y2)Y%2 n Y2)Y+2 n Y2)Y52 � �Rud/ vh ) E%c +c 5� vdwlvid} d htxdêær gh Odsodfh/ hqwær �fdprv frp) E%c +c 5� ' �S[c

txh ì r uhvxowdgr ghvhmdgr1