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!"#$%$&"$&"%'()'*$&"()&)(+,%$&-"".)/,(*,0)1*$"%)"23&'4,"5"6278" 9:;'1,"<" !"#$%&'#()*+$'+!,*-.%+---++ !"#$%$&"$&"%'()'*$&"()&)(+,%$&-"".)/,(*,0)1*$"%)"23&'4,"5"6278" 9:;'1,"=" !"#$%&'()&&"*+'''''''''''''''''''''''''''''''',)*&+#)'-+".'/0&.+"'''''''''''''''''''''''''''''' 1%)$"&*)'2)$.%3"'''''''''''''''''''''''''''''4"&+"'("&)5+$"'6%7%.' !"$*%&.)$'8+59"'*%':5+9%+&"'''''''''''''';"&5"'<"5=>?%+@' !"#$%&'#()*+$'+!,*-.%+---++ <%5)'A)&+=)$@%' B*+@)&"'C24D' EFGG' !"#$%$&"$&"%'()'*$&"()&)(+,%$&-"".)/,(*,0)1*$"%)"23&'4,"5"6278" 9:;'1,">" © 2011, Wagner Corradi; Rodrigo Dias Társia; Leonardo Fonseca; Maria Carolina Nemes; Wanderson Silva de Oliveira; Karla Balzuweit © 2011, Editora UFMG Este livro ou parte dele não pode ser reproduzido por qualquer meio sem a autorização escrita do Editor. Fundamentos de Física I / Wagner Corradi ...[et al.] - Belo Horizonte ; Editora UFMG, 2011 p. – Il (Educação a Distância) Inclui referências. ISBN: 1. Física. 2. Eletricidade. 3. Eletromagnetismo I. Corradi, Wagner II. Série. CDD: CDU: Elaborada pela DITTI – Setor de Tratamento da Informação Biblioteca Universitária da UFMG Este livro recebeu o apoio financeiro da Secretaria de Educação a Distância do MEC. ASSISTÊNCIA EDITORIAL Eliane Sousa e Euclídia Macedo EDITORAÇÃO DE TEXTO Maria do Carmo Leite Ribeiro PREPARAÇÃO DE TEXTO Michel Gannam REVISÃO DE PROVAS FORMATAÇÃO PROJETO GRÁFICO E CAPA Eduardo Ferreira PRODUÇÃO GRÁFICA Warren Marilac EDITORA UFMG Av. Antônio Carlos, 6627 – Ala direita da Biblioteca Central – Térreo Campus Pampulha – 31270-901 – Belo Horizonte/MG Tel.: +55 31 3409-4650 Fax: +55 31 3409-4768 PRÓ-REITORIA DE GRADUAÇÃO Av. Antônio Carlos, 6.627 – Reitoria – 6º andar Campus Pampulha – 31270-901 – Belo Horizonte/MG Tel.: + 55 31 3409-4054 Fax: + 55 31 3409-4060 www..ufmg.br info@prograd.ufmg.br !"#$%$&"$&"%'()'*$&"()&)(+,%$&-"".)/,(*,0)1*$"%)"23&'4,"5"6278" 9:;'1,"?" www.editora.ufmg.br editora@ufmg.br educacaoadistancia@ufmg.br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`:1C4B' TT' IRHE'' (]1(C1:'-:'(I4Q:'B1S/,K(:'QI,I'-K8/,K<CKO_B8'-B'(I,DI'B4'-CI8' -K4B68_B8' T^' IRHM'' (]1(C1:'-:'(I4Q:'B1S/,K(:'QI,I'-K8/,K<CKO_B8'-B'(I,DI'B4'/,a8'-K4B68_B8' ^R' ' Q,:<1B4I8'-I'C6K-I-B' GFV' ' ' ' ' ' ' ' "#-$%$'+@+:+;'-+$'+8%"**+'+*"%*+%?;-.%67'*+ GFW' ' ' ' + %";%+F+:+;'-+$'+8%"**+ GFT' + + + IWHG' 21C\:'-:'(I4Q:'B1S/,K(:' GFT' !"#$%$&"$&"%'()'*$&"()&)(+,%$&-"".)/,(*,0)1*$"%)"23&'4,"5"6278" 9:;'1,"A" IWHE'' I'1BK'-B'DIC88' GGM' IWHM'' 2B,,I4B6/I8'4I/B4]/K(I8b'(]1(C1:'-I'K6/BD,I1'-B'8CQB,2J(KB'6I'1BK'-B' DIC88' GGV' ' QB68B'B',B8Q:6-I' GG^' ' ' ' +++ %";%+G+:+%?;-.%67'*+$%+;'-+$'+8%"**+ GEF' ' ' ' I[HG' (:4:'C8I,'I'1BK'-B'DIC88' GEF' I[HE' IQ1K(IO_B8'-I'1BK'-B'DIC88' GEM' I[HM' (I,DI8'B'(I4Q:'B1S/,K(:8'6I'8CQB,2J(KB'-B'(:6-C/:,B8' GMR' ' QB68B'B',B8Q:6-I' GVM' ' ' ' ' %";%+H+:+%?;-.%67'*+$%+';'(5)*(B(-.%' GVV' ' ' ' ITHG' I/K`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`],KI8'(I,DI8' G[G' IGFHV' 8CQB,2J(KB8'BcCKQ:/B6(KIK8' G[W' ' B\B,(J(K:8'-B'2K\IOP:' GTF' ' ' ' ' %";%+99+:+?)('#.-%;+';<(5-.)+$'+$-*(5-="-67'*+.)#(,#"%*+$'+.%58%+ ';<(5-.%' GTG' ' + ' IGGHG' Q:/B6(KI1'B1S/,K(:'-B'-K8/,K<CKO_B8'(:6/J6CI8'-B'(I,DI+ GTG' IGGHE' Q:/B6(KI1'B1S/,K(:'-B'-K8/,K<CKO_B8'1K6BI,B8'-B'(I,DI' GTE' IGGHM' Q:/B6(KI1'B1S/,K(:'-B'-K8/,K<CKO_B8'8CQB,2K(KIK8'-B'(I,DI' GTW' IGGHV' Q:/B6(KI1'B1S/,K(:'-B'-K8/,K<CKO_B8'`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a6(KI'-:'-KB1S/,K(:' EMM' IGRHE'' ,KDK-BN'-KB1S/,K(I' EMT' IGRHM' I'1BK'-B'DIC88'B':8'-KB1S/,K(:8' EM^' ' QB68B'B',B8Q:6-IU'B\B,(J(K:8'-B'2K\IOP:' EV[' ' ' ' ' %";%+9F+:+M'()5'*+$'*;).%&'#()+';<(5-.)+'+?);%5-N%6C)+';<(5-.%' EV^' ' + ' IGWHG' :8'`B/:,B8'Q:1I,KNIOP:'B'-B81:(I4B6/:'B1S/,K(:' EV^' ' QB68B'B',B8Q:6-I' ERV' ' ' ' ' %";%+9G+:+(5%=%;J)+'+'#'58-%+$'+$-*(5-="-67'*+$'+.%58%' ERR' ' + ' IG[HG' /,I<I1A:'B'B6B,DKI'-B'C4I'-K8/,K<CKOP:'-K8(,B/I'-B'(I,DI8' ERR' IG[HE' /,I<I1A:'B'B6B,DKI'-B'C4I'-K8/,K<CKOP:'-K8(,B/I'-B'(I,DI8' ER^' IG[HM' -B68K-I-B'-B'B6B,DKI' EWG' IG[HV' C4I'IQI,B6/B'K6(:68K8/a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a6(KI'B1S/,K(I' E^F' IG^HE' 1BK'-B':A4' E^G' IG^HM' ,B8K8/K`K-I-B'B'(:6-C/K`K-I-B' E^R' ' QB68B'B',B8Q:6-I'B'B\B,(J(K:8'-B'2K\IOP:' E^[' ' ' ' ' ' ' ' %";%+>L+:5'*-*(-M-$%$'+$)*+&%('5-%-*+'+?)(E#.-%+';<(5-.%' MFF' ' + ' IEFHG' ,B8K8/K`K-I-B'B'B2BK/:'-I'/B4QB,I/C,I' MFF' IEFHE' Q:/a6(KI'B4'(K,(CK/:8'B1S/,K(:8' MFE' ' QB68B'B',B8Q:6-I'B'B\B,(J(K:8'-B'2K\IOP:' MF[' ' ' ' ' %";%+>9+:+.)#$"()5'*K+$-';<(5-.)*+'+*'&-.)#$"()5'*' MFT' ' + ' IEGHG' `K8P:'4K(,:8(XQK(I'-I'(:6-COP:'B1S/,K(I' MFT' ' QB68B'B',B8Q:6-I'B'Q,:<1B4I8'-I'C6K-I-B'MGE' ' ' ' ' ' ' + "#-$%$'+G+:+.-5."-()*+$'+.)55'#('+.)#(,#"%++ MGV' ' ' ' ' %";%+>>+:+;'-*+$'+O-5.J)!!' MGW' ' + ' IEEHG' 1BK'-I8'4I1AI8' MGW' IEEHE' 1BK'-:8'6X8' MG^' ' QB68B'B',B8Q:6-I'B'B\B,(J(K:8'-B'2K\IOP:' MMF' ' ' ' ' %";%+>@+:.-5."-()*+$'+&%-*+$'+"&%+&%;J%' MME' ' + ' IEMHG' (K,(CK/:8'B1S/,K(:8' MME' ' QB68B'B',B8Q:6-I'B'B\B,(J(K:8'-B'2K\IOP:' MMT' ' ' ' ' ' ' ' !"#$%$&"$&"%'()'*$&"()&)(+,%$&-"".)/,(*,0)1*$"%)"23&'4,"5"6278" 9:;'1,"C" ' %";%+>A+:%?%5';J)*+$'+&'$-$%+-' MVF' ' + ' IEVHG' DI1`I6Y4B/,:' MVF' IEVHE' I4QB,J4B/,:' MVM' ' B\B,(J(K:8'-B'2K\IOP:' MVR' ' ' ' ' %";%+>D+:+%?%5';J)*+$'+&'$-$%+--' MV[' ' + ' IERHG' `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cCB'B4'(K,(CK/:8'B1S/,K(:8' VFF' ' B\B,(J(K:8'-B'2K\IOP:'B'Q,:<1B4I8'-I'C6K-I-B' VF[' ' ' ' ' ' ' + "#-$%$'+I+:+!)#('*+$'+.%&?)+&%8#<(-.)+'+%+;'-+$'+%&?P5'++ VF^' + + ' + %";%+>I+%+;'-+$'+=-)(Q*%M%5(+ VGG' + + ' IE^HG' I'1BK'-B'<K:/d8I`I,/' VGG' IE^HE' 2:,OI'B6/,B'2K:8'QI,I1B1:8' VGT' IE^HM' (I4Q:'4ID6S/K(:'DB,I-:'Q:,'(I,DI'B4'4:`K4B6/:' VG^' ' B\B,(J(K:8'-B'2K\IOP:' VEV' ' ' ' + %";%+@L+.%&?)+&%8#<(-.)+'&+*);'#R-$'*+ VEW' + + ' IMFHG' (I4Q:'4ID6S/K(:'DB,I-:'Q:,'C4I'B8QK,I' VEW' IMFHE' -B8(,KOP:'-:'(I4Q:'4ID6S/K(:'DB,I-:'Q:,'C4'8:1B6XK-B' VMW' ' B\B,(J(K:8'-B'2K\IOP:'B'Q,:<1B4I8'-I'C6K-I-B' VVF' + + ' + %";%+@9+;'-+$'+%&?P5'+ VVE' + + ' IMGHG' I'1BK'-B'I4Qe,B' ' ' B\B,(J(K:8'-B'2K\IOP:'B'Q,:<1B4I8'-I'C6K-I-B' VR[' ' ' ' ' ' ' + "#-$%$'+9L+:+;'-*+$'+!%5%$%S+'+$'+;'#N+'+%+-#$"6C)+';'(5)&%8#<(-.%+ VRT' + + ' + %";%+@>+;'-+$'+!%5%$%S+'+;'-+$'+;'#N+ VWF' + + ' IMEHG' :'21C\:'-I'K6-COP:'4ID6S/K(I' VWF' IMEHE' I'1BK'-B'2I,I-If' VWG' IMEHM' I'1BK'-B'1B6N' VWV' IMEHV' B8/C-:'cCI6/K/I/K`:'-I'1BK'-B'2I,I-If' ' !"#$%$&"$&"%'()'*$&"()&)(+,%$&-"".)/,(*,0)1*$"%)"23&'4,"5"6278" 9:;'1,"D" IMEHR' 2:,OI'B1B/,:4:/,KN'B'(:,,B6/B'K6-CNK-I' V[T' IMEHW' DB,I-:,B8'B'4:/:,B8' VTG' ' B\B,(J(K:8'-B'2K\IOP:' VTW' + + ' + %";%+@@+.%&?)+';<(5-.)+M%5-BM';+.)&+)+('&?)+ VTT' + + ' IMMHG' :'(I4Q:'B1S/,K(:'K6-CNK-:' VTT' IMMHE' (:,,B6/B8'-B'2:C(IC1/' V^R' IMMHM' I'K6-COP:'B':'4:`K4B6/:',B1I/K`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g/CI' REE' ' B\B,(J(K:8'-B'2K\IOP:'B'Q,:<1B4I8'-I'C6K-I-B' RMG' ' ' ' ' ' ' + "#-$%$'+9>+:+)*.-;%67'*+';'(5)&%8#<(-.%*+'+.-5."-()*+$'+.)55'#('+ %;('5#%$%+ RMV' + + ' + %";%+@F+)*.-;%67'*+'&+.-5."-()*+';<(5-.)*+-+ RMW' + + ' IMWHG' :'(K,(CK/:'1(' RMW' IMWHE' B6B,DKI'6:'(K,(CK/:'1(' RVV' ' B\B,(J(K:8'-B'2K\IOP:' RRF' ' ' ' + + ' + %";%+@G+)*.-;%67'*+'&+.-5."-()*+';<(5-.)*+--+ RRM' 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