{"id":1648,"date":"2015-12-19T14:53:36","date_gmt":"2015-12-19T14:53:36","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=1648"},"modified":"2024-08-20T15:45:34","modified_gmt":"2024-08-20T15:45:34","slug":"superficies-equipotenciais-trabalho-da-forca-eletrostatica","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/eletricidade\/eletrostatica\/superficies-equipotenciais-trabalho-da-forca-eletrostatica\/","title":{"rendered":"Superf\u00edcies Equipotenciais \u2013 Trabalho da For\u00e7a Eletrost\u00e1tica"},"content":{"rendered":"

Superf\u00edcies Equipotenciais \u2013 Trabalho da For\u00e7a Eletrost\u00e1tica<\/b><\/span><\/span><\/span><\/p>\n

Define-se <\/b><\/span><\/span><\/span>superf\u00edcie equipotencial de um campo el\u00e9trico<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>qualquer superf\u00edcie em cujos pontos o <\/b><\/span><\/span><\/span>potencial el\u00e9trico \u00e9 constante.<\/b><\/span><\/span><\/span><\/p>\n

Estas superf\u00edcies t\u00eam duas propriedades importantes:
\n<\/b><\/span><\/span><\/span><\/p>\n

\"\" A <\/b><\/span><\/span><\/span>for\u00e7a el\u00e9trica durante o deslocamento de uma carga el\u00e9trica puntiforme sobre uma superf\u00edcie equipotencial \u00e9 nula.<\/b><\/span><\/span><\/span><\/p>\n

As <\/b><\/span><\/span><\/span>superf\u00edcies equipotenciais s\u00e3o perpendiculares \u00e0s linhas de for\u00e7a ou linhas de campo el\u00e9trico <\/b><\/span><\/span><\/span>e, conseq\u00fcentemente, <\/b><\/span><\/span><\/span>perpendiculares ao vetor campo el\u00e9trico\u00a0\"\"<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Superf\u00edcies equipotenciais e linhas de for\u00e7a de uma carga puntiforme Q<\/b><\/span><\/span><\/span><\/p>\n

No <\/b><\/span><\/span><\/span>caso particular do campo de uma carga puntiforme Q<\/b><\/span><\/span><\/span>, a <\/b><\/span><\/span><\/span>simetria <\/b><\/span><\/span><\/span>sugere as <\/b><\/span><\/span><\/span>superf\u00edcies equipotenciais<\/b><\/span><\/span><\/span> s\u00e3o <\/b><\/span><\/span><\/span>superf\u00edcies esf\u00e9ricas conc\u00eantricas<\/b><\/span><\/span><\/span> com a <\/b><\/span><\/span><\/span>carga Q<\/b><\/span><\/span><\/span> e as<\/b><\/span><\/span><\/span>linhas de for\u00e7a (de campo) s\u00e3o radiais com o centro da carga.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe nas <\/b><\/span><\/span><\/span>figuras acima<\/b><\/span><\/span><\/span> que as <\/b><\/span><\/span><\/span>linhas de for\u00e7a (de campo)<\/b><\/span><\/span><\/span> se <\/b><\/span><\/span><\/span>afastam<\/b><\/span><\/span><\/span> das <\/b><\/span><\/span><\/span>cargas positivas<\/b><\/span><\/span><\/span> e nas <\/b><\/span><\/span><\/span>figuras abaixo<\/b><\/span><\/span><\/span> se <\/b><\/span><\/span><\/span>aproximam <\/b><\/span><\/span><\/span>das <\/b><\/span><\/span><\/span>negativas.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Para cargas <\/b><\/span><\/span><\/span>positivas, o <\/b><\/span><\/span><\/span>potencial de cada superf\u00edcie<\/b><\/span><\/span><\/span> <\/b>aumenta<\/b><\/span><\/span><\/span> quando se <\/b><\/span><\/span><\/span>aproxima da carga<\/b><\/span><\/span><\/span> <\/b>e para <\/b><\/span><\/span><\/span>cargas negativas diminui quando se afasta da carga.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Nas figuras abaixo est\u00e3o representados v\u00e1rias configura\u00e7\u00f5es com as respectivas linhas de for\u00e7a e superf\u00edcies equipotenciais<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"\u00a0<\/span><\/p>\n

Superf\u00edcies equipotenciais de um <\/b><\/span><\/span><\/span>Campo El\u00e9trico Uniforme<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Um campo <\/b><\/span><\/span><\/span>el\u00e9trico uniforme tem em todos os seus infinitos pontos mesma intensidade, mesma dire\u00e7\u00e3o e mesmo sentido e \u00e9 <\/b><\/span><\/span><\/span>obtido <\/b><\/span><\/span><\/span>entre duas placas condutoras id\u00eanticas<\/b><\/span><\/span><\/span> e paralelas e <\/b><\/span><\/span><\/span>eletrizadas com cargas de mesmo m\u00f3dulo, mas de sinais contr\u00e1rios.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe, na figura acima, <\/b><\/span><\/span><\/span>que nesse caso as <\/b><\/span><\/span><\/span>superf\u00edcies equipotenciais\u00a0 s\u00e3o planas e paralelas entre si.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Trabalho (W) e diferen\u00e7a de potencial (U)<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Considere o <\/b><\/span><\/span><\/span>campo el\u00e9trico criado por uma carga fonte puntiforme Q (figura I)<\/b><\/span><\/span><\/span> e o <\/b><\/span><\/span><\/span>campo el\u00e9trico<\/b><\/span><\/span><\/span> <\/b>uniforme criado por duas placas condutoras id\u00eanticas e paralelas e eletrizadas com cargas de<\/b><\/span><\/span><\/span> <\/b>mesmo m\u00f3dulo, mas de sinais contr\u00e1rios (figura II).<\/b><\/span><\/span><\/span><\/b><\/p>\n

\"\"<\/p>\n

\u00a0Uma <\/b><\/span><\/span><\/span>part\u00edcula de prova q,<\/b><\/span><\/span><\/span> <\/b>abandonada\u00a0 no interior desses campos, fica sujeita a uma for\u00e7a\u00a0\"\", que a faz se deslocar do ponto R (de potencial V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>) para o ponto S (de potencial V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

Figura I<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>campo el\u00e9trico vari\u00e1vel<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 sendo a <\/b><\/span><\/span><\/span>for\u00e7a\u00a0\"\"\u00a0conservativa<\/b><\/span><\/span><\/span>, o <\/b><\/span><\/span><\/span>trabalho <\/b><\/span><\/span><\/span>por ela realizado \u00e9 fornecido pela <\/b><\/span><\/span><\/span>varia\u00e7\u00e3o<\/b><\/span><\/span><\/span> <\/b>de energia potencial el\u00e9trica (inicial menos final)<\/b><\/span><\/span><\/span>\u00a0 \"\" <\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>RS<\/b><\/span><\/span><\/sub><\/span>= E<\/b><\/span><\/span><\/span>pR<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 E<\/b><\/span><\/span><\/span>pS<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 E<\/b><\/span><\/span><\/span>pR <\/b><\/span><\/span><\/sub><\/span>= q.V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 E<\/b><\/span><\/span><\/span>pS <\/b><\/span><\/span><\/sub><\/span>= q.V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 W<\/b><\/span><\/span><\/span>RS<\/b><\/span><\/span><\/sub><\/span>= qV<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 qV<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>RS<\/b><\/span><\/span><\/sub><\/span>= q(V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>)\u00a0 ou\u00a0 W<\/b><\/span><\/span><\/span>RS <\/b><\/span><\/span><\/sub><\/span>= qU<\/b><\/span><\/span><\/span>RS,<\/b><\/span><\/span><\/sub><\/span>\u00a0onde\u00a0<\/b><\/span><\/span><\/span><\/p>\n

U<\/b><\/span><\/span><\/span>RS <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Figura II<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>campo el\u00e9trico uniforme<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 sendo a <\/b><\/span><\/span><\/span>for\u00e7a\u00a0\"\"\u00a0conservativa<\/b><\/span><\/span><\/span>, o <\/b><\/span><\/span><\/span>trabalho <\/b><\/span><\/span><\/span>por ela realizado \u00e9 <\/b><\/span><\/span><\/span>fornecido pela varia\u00e7\u00e3o de energia potencial el\u00e9trica (inicial menos final)<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 W<\/b><\/span><\/span><\/span>RS <\/b><\/span><\/span><\/sub><\/span>= E<\/b><\/span><\/span><\/span>pR<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 E<\/b><\/span><\/span><\/span>pS<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 E<\/b><\/span><\/span><\/span>pR<\/b><\/span><\/span><\/sub><\/span>q.V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 E<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>q.V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 W<\/b><\/span><\/span><\/span>RS <\/b><\/span><\/span><\/sub><\/span>= qV<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 qV<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>RS <\/b><\/span><\/span><\/sub><\/span>= q(V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>) ou\u00a0 W<\/b><\/span><\/span><\/span>RS<\/b><\/span><\/span><\/sub><\/span>=qU<\/b><\/span><\/span><\/span>RS<\/b><\/span><\/span><\/sub><\/span>\u00a0 onde\u00a0 <\/b><\/span><\/span><\/span>U<\/b><\/span><\/span><\/span>RS <\/b><\/span><\/span><\/sub><\/span>=<\/b><\/span><\/span><\/span> <\/b>V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Mas, o <\/b><\/span><\/span><\/span>trabalho da for\u00e7a el\u00e9trica tamb\u00e9m \u00e9 fornecido por<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>RS <\/b><\/span><\/span><\/sub><\/span>= F.RS.cos\u03b8 <\/b><\/span><\/span><\/span>= F.RS.d\/RS\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>RS <\/b><\/span><\/span><\/sub><\/span>=<\/b><\/span><\/span><\/span> <\/b>F.d<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 E=F\/q\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>F = q.E<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 W<\/b><\/span><\/span><\/span>RS <\/b><\/span><\/span><\/sub><\/span>= q.E.d\u00a0 \"\"\u00a0 q(V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>) = q.E.d\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>(V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>) = E.d\u00a0 <\/b><\/span><\/span><\/span>ou\u00a0<\/b><\/span><\/span><\/span><\/p>\n

U<\/b><\/span><\/span><\/span>RS <\/b><\/span><\/span><\/sub><\/span>= E.d<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Observe atentamente o formul\u00e1rio abaixo com as express\u00f5es do trabalho W e da diferen\u00e7a de potencial U de um campo el\u00e9trico vari\u00e1vel e de um campo el\u00e9trico uniforme<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"\u00a0Observe nas <\/b><\/span><\/span><\/span>figuras I e II,<\/b><\/span><\/span><\/span> onde as <\/b><\/span><\/span><\/span>curvas representam as superf\u00edcies equipotenciais<\/b><\/span><\/span><\/span>, as <\/b><\/span><\/span><\/span>retas vermelhas as linhas de campo (de for\u00e7a)<\/b><\/span><\/span><\/span> <\/b>geradas<\/b><\/span><\/span><\/span> por uma <\/b><\/span><\/span><\/span>carga fonte positiva Q <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>q, uma carga de prova se deslocando no interior desse campo, em <\/b><\/span><\/span><\/span>que:<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\u00a0\"\"<\/span><\/p>\n

\u00a0<\/span>Cargas el\u00e9tricas positivas (q)<\/b><\/span><\/span><\/span> se movem <\/b><\/span><\/span><\/span>espontaneamente (W > 0) no sentido dos potenciais menores.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Cargas el\u00e9tricas negativas (-q)<\/b><\/span><\/span><\/span> se movem <\/b><\/span><\/span><\/span>espontaneamente (W > 0) no sentido dos potenciais maiores.<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>sentido <\/b><\/span><\/span><\/span>do <\/b><\/span><\/span><\/span>campo el\u00e9trico<\/b><\/span><\/span><\/span> \u00e9 <\/b><\/span><\/span><\/span>sempre <\/b><\/span><\/span><\/span>do <\/b><\/span><\/span><\/span>maior para o menor potencial.<\/b><\/span><\/span><\/span><\/p>\n

As <\/b><\/span><\/span><\/span>tr\u00eas observa\u00e7\u00f5es acima<\/b><\/span><\/span><\/span> tamb\u00e9m <\/b><\/span><\/span><\/span>s\u00e3o v\u00e1lidas <\/b><\/span><\/span><\/span>se o <\/b><\/span><\/span><\/span>campo el\u00e9trico for uniforme<\/b><\/span><\/span><\/span> conforme voc\u00ea pode observar na <\/b><\/span><\/span><\/span>figura abaixo,<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

onde no <\/b><\/span><\/span><\/span>interior do campo el\u00e9trico uniforme<\/b><\/span><\/span><\/span> criado pela <\/b><\/span><\/span><\/span>placas eletrizadas A e B,<\/b><\/span><\/span><\/span> com <\/b><\/span><\/span><\/span>potenciais V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0e<\/b><\/span><\/span><\/span> <\/b>V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>(V<\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/sub><\/span>> V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span> existe uma solu\u00e7\u00e3o de NaCl em \u00e1gua com <\/b><\/span><\/span><\/span>\u00edons negativos se movendo no sentido da placa positiva e \u00edons positivos no sentido da placa negativa.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Unidades do campo el\u00e9trico<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 da express\u00e3o <\/b><\/span><\/span><\/span>E=F\/q,<\/b><\/span><\/span><\/span> o campo tem <\/b><\/span><\/span><\/span>unidades no SI<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0\u00a0 <\/b><\/span><\/span><\/span>newton\/Coulomb = N\/C<\/b><\/span><\/span><\/span>\u00a0 \"\" outra unidade \u00a0\"\" da express\u00e3o <\/b><\/span><\/span><\/span>U=E.d<\/b><\/span><\/span><\/span>, o campo el\u00e9trico tem <\/b><\/span><\/span><\/span>unidades no SI<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>volt\/metro (V\/m).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>El\u00e9tron-volt (eV)<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 corresponde ao <\/b><\/span><\/span><\/span>trabalho realizado, quando 1 el\u00e9tron abandonado do<\/b><\/span><\/span><\/span> <\/b>repouso em um ponto A de um campo el\u00e9trico, desloca-se espontaneamente at\u00e9 um ponto B, de modo que V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>B <\/b><\/span><\/span><\/sub><\/span>= 1V\u00a0<\/b><\/span><\/span><\/span> \"\"\u00a0 <\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>AB<\/b><\/span><\/span><\/sub><\/span>=q(V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>) <\/b><\/span><\/span><\/span>= 1,6.10<\/b><\/span><\/span><\/span>-19<\/b><\/span><\/span><\/sup><\/span>.1\u00a0 \"\" <\/b><\/span><\/span><\/span>1 eV=1,6.10<\/b><\/span><\/span><\/span>-19<\/b><\/span><\/span><\/sup><\/span>J.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Pela express\u00e3o <\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>AB <\/b><\/span><\/span><\/sub><\/span>= q(V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>),<\/b><\/span><\/span><\/span> se os <\/b><\/span><\/span><\/span>pontos A e B estiverem sobre a mesma superf\u00edcie<\/b><\/span><\/span><\/span> <\/b>equipotencial (V<\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>B <\/b><\/span><\/span><\/sub><\/span>= V),<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>trabalho da for\u00e7a el\u00e9trica nesse deslocamento ser\u00e1 nulo <\/b><\/span><\/span><\/span>pois, <\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>AB<\/b><\/span><\/span><\/sub><\/span> = q.(V \u2013 V) = q.0 = 0.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

O que voc\u00ea deve saber, informa\u00e7\u00f5es e dicas<\/b><\/span><\/span><\/span><\/p>\n

Superf\u00edcies equipotenciais e linhas de for\u00e7a de uma carga puntiforme Q<\/b><\/span><\/span><\/span><\/p>\n

No <\/b><\/span><\/span><\/span>caso particular do campo de uma carga puntiforme Q<\/b><\/span><\/span><\/span>, a <\/b><\/span><\/span><\/span>simetria <\/b><\/span><\/span><\/span>sugere as <\/b><\/span><\/span><\/span>superf\u00edcies equipotenciais<\/b><\/span><\/span><\/span> s\u00e3o <\/b><\/span><\/span><\/span>superf\u00edcies esf\u00e9ricas conc\u00eantricas<\/b><\/span><\/span><\/span> com a <\/b><\/span><\/span><\/span>carga Q<\/b><\/span><\/span><\/span> e as<\/b><\/span><\/span><\/span>linhas de for\u00e7a (de campo) s\u00e3o radiais com o centro da carga.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe nas <\/b><\/span><\/span><\/span>figuras acima<\/b><\/span><\/span><\/span> que as <\/b><\/span><\/span><\/span>linhas de for\u00e7a (de campo)<\/b><\/span><\/span><\/span> se <\/b><\/span><\/span><\/span>afastam<\/b><\/span><\/span><\/span> das <\/b><\/span><\/span><\/span>cargas positivas<\/b><\/span><\/span><\/span> e nas <\/b><\/span><\/span><\/span>figuras abaixo<\/b><\/span><\/span><\/span> se <\/b><\/span><\/span><\/span>aproximam <\/b><\/span><\/span><\/span>das <\/b><\/span><\/span><\/span>negativas.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"\u00a0Para cargas <\/b><\/span><\/span><\/span>positivas, o <\/b><\/span><\/span><\/span>potencial de cada superf\u00edcie<\/b><\/span><\/span><\/span> <\/b>aumenta<\/b><\/span><\/span><\/span> quando se <\/b><\/span><\/span><\/span>aproxima da carga<\/b><\/span><\/span><\/span> <\/b>e para <\/b><\/span><\/span><\/span>cargas negativas diminui quando se afasta da carga.<\/b><\/span><\/span><\/span><\/p>\n

Nas figuras abaixo est\u00e3o representados v\u00e1rias configura\u00e7\u00f5es com as respectivas linhas de for\u00e7a e superf\u00edcies equipotenciais<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\u00a0\u00a0\"\"<\/span><\/p>\n

\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\u00a0<\/span><\/p>\n

\"\" \u00a0<\/span>Unidades do campo el\u00e9trico<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 da express\u00e3o <\/b><\/span><\/span><\/span>E=F\/q,<\/b><\/span><\/span><\/span> o campo tem <\/b><\/span><\/span><\/span>unidades no SI<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0\u00a0 <\/b><\/span><\/span><\/span>newton\/Coulomb = N\/C<\/b><\/span><\/span><\/span>\u00a0 \"\" outra unidade \u00a0\"\" da express\u00e3o <\/b><\/span><\/span><\/span>U=E.d<\/b><\/span><\/span><\/span>, o campo el\u00e9trico tem <\/b><\/span><\/span><\/span>unidades no SI<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>volt\/metro (V\/m).<\/b><\/span><\/span><\/span><\/p>\n

\"\" \u00a0<\/span>El\u00e9tron-volt (eV)<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 corresponde ao <\/b><\/span><\/span><\/span>trabalho realizado, quando 1 el\u00e9tron abandonado do<\/b><\/span><\/span><\/span> <\/b>repouso em um ponto A de um campo el\u00e9trico, desloca-se espontaneamente at\u00e9 um ponto B, de modo que V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>B <\/b><\/span><\/span><\/sub><\/span>= 1V\u00a0<\/b><\/span><\/span><\/span> \"\"\u00a0 <\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>AB<\/b><\/span><\/span><\/sub><\/span>=q(V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>) <\/b><\/span><\/span><\/span>= 1,6.10<\/b><\/span><\/span><\/span>-19<\/b><\/span><\/span><\/sup><\/span>.1\u00a0 \"\" <\/b><\/span><\/span><\/span>1 eV=1,6.10<\/b><\/span><\/span><\/span>-19<\/b><\/span><\/span><\/sup><\/span>J.<\/b><\/span><\/span><\/span><\/p>\n

\"\" \u00a0Pela express\u00e3o <\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>AB <\/b><\/span><\/span><\/sub><\/span>= q(V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>),<\/b><\/span><\/span><\/span> se os <\/b><\/span><\/span><\/span>pontos A e B estiverem sobre a mesma superf\u00edcie<\/b><\/span><\/span><\/span> <\/b>equipotencial (V<\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>B <\/b><\/span><\/span><\/sub><\/span>= V),<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>trabalho da for\u00e7a el\u00e9trica nesse deslocamento ser\u00e1 nulo <\/b><\/span><\/span><\/span>pois, <\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>AB<\/b><\/span><\/span><\/sub><\/span> = q.(V \u2013 V) = q.0 = 0.<\/b><\/span><\/span><\/span><\/p>\n

Confira os exerc\u00edcios com resolu\u00e7\u00e3o comentada<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Superf\u00edcies Equipotenciais \u2013 Trabalho da For\u00e7a Eletrost\u00e1tica Define-se superf\u00edcie equipotencial de um campo el\u00e9trico a qualquer superf\u00edcie em cujos pontos o potencial el\u00e9trico \u00e9 constante. Estas superf\u00edcies t\u00eam duas propriedades importantes: A for\u00e7a el\u00e9trica durante o deslocamento de uma carga el\u00e9trica puntiforme sobre uma superf\u00edcie equipotencial \u00e9 nula. As superf\u00edcies equipotenciais s\u00e3o perpendiculares \u00e0s linhas de for\u00e7a ou linhas de<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":193,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-1648","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1648","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=1648"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1648\/revisions"}],"predecessor-version":[{"id":1654,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1648\/revisions\/1654"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/193"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=1648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}