{"id":41645,"date":"2021-10-15T11:24:05","date_gmt":"2021-10-15T14:24:05","guid":{"rendered":"https:\/\/www.antonioguilherme.web.br.com\/blog\/?page_id=41645"},"modified":"2025-09-23T15:57:52","modified_gmt":"2025-09-23T18:57:52","slug":"constante-dieletrica","status":"publish","type":"page","link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/","title":{"rendered":"Constante Diel\u00e9trica"},"content":{"rendered":"<h2 id='introdu\u00e7\u00e3o'  id=\"boomdevs_1\"><span style=\"font-family: verdana, geneva, sans-serif;\">Introdu\u00e7\u00e3o<\/span><\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A<strong> Constante Diel\u00e9trica ou Permissividade El\u00e9trica Relativa -\u03b5<\/strong><strong><sub>r<\/sub><\/strong>&#8211; consiste na capacidade do material de armazenar cargas el\u00e9tricas e traduz, de forma macrosc\u00f3pica, os efeitos que ocorrem no interior de \u00e1tomos e mol\u00e9culas devido ao campo el\u00e9trico. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, ela se encontra diretamente relacionada \u00e0 estrutura da mat\u00e9ria, e<\/span><span style=\"font-family: verdana, geneva, sans-serif;\"> varia em mais de 4 ordens de magnitude dependendo do material.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> <!-- \/wp:post-content -->\r\n\r\n<!-- wp:paragraph --> <\/span> <span style=\"font-family: verdana, geneva, sans-serif;\">Nos gases, em decorr\u00eancia da dist\u00e2ncia entre mol\u00e9culas, que resulta em densidades baixas, a constante diel\u00e9trica permanece um pouco maior do que a constante diel\u00e9trica do v\u00e1cuo. Por exemplo, a constante diel\u00e9trica do ar na press\u00e3o de 1 atm vale 1,000 6.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> <!-- \/wp:paragraph -->\r\n\r\n<!-- wp:paragraph --> <\/span> <span style=\"font-family: verdana, geneva, sans-serif;\">Na maioria das cer\u00e2micas e pol\u00edmeros, a constante diel\u00e9trica varia entre 2 e 10 em decorr\u00eancia das liga\u00e7\u00f5es covalentes.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> <!-- \/wp:paragraph -->\r\n\r\n<!-- wp:paragraph --> <\/span> <span style=\"font-family: verdana, geneva, sans-serif;\">No caso de materiais com liga\u00e7\u00f5es i\u00f4nicas, a constante diel\u00e9trica se encontra entre 6 e 10.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Materiais com elevados valores de constante diel\u00e9trica possuem mecanismos especiais de polariza\u00e7\u00e3o que envolvem a rota\u00e7\u00e3o de dipolos ou transforma\u00e7\u00e3o ferroel\u00e9trica de fase. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A \u00e1gua, com constante diel\u00e9trica de 80, e o BaTiO3, com constate diel\u00e9trica de 1 000, s\u00e3o exemplos desses mecanismos.<\/span><\/p>\r\n<h2 id='efeitos-do-campo-el\u00e9trico-nos-materiais'  id=\"boomdevs_2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Efeitos do Campo El\u00e9trico nos Materiais<\/span><\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A eletricidade surgiu antes da descoberta do el\u00e9tron e, consequentemente, desenvolveram-se teorias macrosc\u00f3picas e experimentais para explicar os efeitos do campo el\u00e9trico nos materiais.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Posteriormente, passou-se a utilizar as te\u00f3ricas sobre a estrutura da mat\u00e9ria para explicar o comportamento dos materiais sob campos el\u00e9tricos.<\/span><\/p>\r\n<h3 id='comportamento-macrosc\u00f3pico'  id=\"boomdevs_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">Comportamento Macrosc\u00f3pico<\/span><\/h3>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"><!-- \/wp:paragraph -->\r\n\r\n<!-- wp:paragraph --><\/span><span style=\"font-family: verdana, geneva, sans-serif;\">O Eletromagnetismo explica de forma macrosc\u00f3pica a influ\u00eancia do campo el\u00e9trico nos materiais atrav\u00e9s da cria\u00e7\u00e3o do vetor de <strong>Polariza\u00e7\u00e3o &#8211; P<\/strong>, que re\u00fane macroscopicamente os efeitos do campo el\u00e9trico nos materiais de acordo com a Figura 1.<\/span><\/p>\r\n<figure id=\"attachment_41513\" aria-describedby=\"caption-attachment-41513\" style=\"width: 800px\" class=\"wp-caption alignnone\"><img decoding=\"async\" class=\"wp-image-41513 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/Polarizacao.jpg\" alt=\"\" width=\"800\" height=\"640\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/Polarizacao.jpg 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/Polarizacao-300x240.jpg 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/Polarizacao-768x614.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-41513\" class=\"wp-caption-text\">Figura 1. Vetor Polariza\u00e7\u00e3o<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 1 mostra a rela\u00e7\u00e3o do vetor P com os vetores densidade de campo el\u00e9trico e densidade de fluxo el\u00e9trico.<\/span><\/p>\r\n<figure id=\"attachment_41519\" aria-describedby=\"caption-attachment-41519\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41519 size-medium\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/polarizacao_1-300x236.png\" alt=\"\" width=\"300\" height=\"236\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/polarizacao_1-300x236.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/polarizacao_1.png 312w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-41519\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 1. Densidade de fluxo el\u00e9trico<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">D \u00e9 o vetor densidade de fluxo el\u00e9trico [C\/m<sup>2<\/sup>];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">E \u00e9 o vetor densidade de campo el\u00e9trico [V\/m];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">P \u00e9 o vetor de polariza\u00e7\u00e3o el\u00e9trica [C\/m<sup>2<\/sup>];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5<sub>0 <\/sub>\u00e9 a <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/constantes-fisicas\/\">permissividade do v\u00e1cuo<\/a> [F\/m];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c7<sub>e<\/sub> \u00e9 a suscetibilidade el\u00e9trica do material;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5<sub>r<\/sub> \u00e9 a permissividade relativa do material.<\/span><\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 2 mostra a rela\u00e7\u00e3o entre o vetor de polariza\u00e7\u00e3o, o campo el\u00e9trico e a propriedade do material expressa em fun\u00e7\u00e3o de uma propriedade macrosc\u00f3pica do material denominada suscetibilidade el\u00e9trica.<\/span><\/p>\r\n<figure id=\"attachment_41521\" aria-describedby=\"caption-attachment-41521\" style=\"width: 243px\" class=\"wp-caption alignnone\"><img decoding=\"async\" class=\"size-full wp-image-41521\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/polarizacao_2.png\" alt=\"\" width=\"243\" height=\"51\" \/><figcaption id=\"caption-attachment-41521\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 2. Vetor polariza\u00e7\u00e3o<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por sua vez, a Equa\u00e7\u00e3o 3 apresenta a rela\u00e7\u00e3o entre as duas outras maneiras de relacionar a susceptibilidade el\u00e9trica com a permissibilidade el\u00e9trica ou constante diel\u00e9trica dos materiais relativa e absoluta.\u00a0<\/span><\/p>\r\n<figure id=\"attachment_41523\" aria-describedby=\"caption-attachment-41523\" style=\"width: 300px\" class=\"wp-caption alignnone\"><img decoding=\"async\" class=\"size-medium wp-image-41523\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/polarizacao_3-300x181.png\" alt=\"\" width=\"300\" height=\"181\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/polarizacao_3-300x181.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/polarizacao_3.png 305w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-41523\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 3. Permissividade el\u00e9trica e susceptibilidade el\u00e9trica.<\/figcaption><\/figure>\r\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span> <span style=\"font-family: verdana, geneva, sans-serif;\"> <!-- \/wp:paragraph -->\r\n\r\n<!-- wp:list --> <\/span>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">D \u00e9 a densidade do fluxo el\u00e9trico [C\/m<sup>2<\/sup>];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">P \u00e9 o vetor de polariza\u00e7\u00e3o [C\/m<sup>2<\/sup>];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">E \u00e9 a intensidade do campo el\u00e9trico [V\/m];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5 \u00e9 a permissividade el\u00e9trica ou constante diel\u00e9trica do material [F\/m];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5<sub>0<\/sub> \u00e9 a permissividade ou constante diel\u00e9trica do v\u00e1cuo [8,854 187 817 81 x 10<sup>-12<\/sup> F\/m];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5<sub>r <\/sub>\u00e9 a permissividade ou constante diel\u00e9trica relativa do material;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c7<sub>e<\/sub> \u00e9 a susceptibilidade el\u00e9trica do material.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/figure>\r\n<figure><span style=\"font-family: verdana, geneva, sans-serif;\">As permissividades absolutas possuem valores num\u00e9ricos pequenos expressos em F\/m que dificultam o trabalho de compara\u00e7\u00e3o entre materiais. Por isso, utiliza-se a permissividade relativa e a susceptibilidade.<\/span><\/figure>\r\n<figure><\/figure>\r\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><span style=\"font-family: verdana, geneva, sans-serif;\">Observa-se que a presen\u00e7a de mat\u00e9ria sempre aumenta a densidade de fluxo el\u00e9trico &#8211; D, e a<\/span><span style=\"font-family: verdana, geneva, sans-serif;\">\u00a0constante diel\u00e9trica \u00e9 tudo menos uma constante. <\/span><\/figure>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Ela depende da frequ\u00eancia e intensidade do campo el\u00e9trico, da temperatura, da press\u00e3o e da estrutura do material. <\/span><\/p>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Ao se considerar a frequ\u00eancia do campo el\u00e9trico aplicado, a constante diel\u00e9trica se torna uma grandeza complexa, possuindo uma parte real e outra imagin\u00e1ria, conforme mostra a Equa\u00e7\u00e3o 7.<\/span><\/p>\r\n<figure id=\"attachment_41663\" aria-describedby=\"caption-attachment-41663\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41663 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/droppedImage.png\" alt=\"\" width=\"300\" height=\"93\" \/><figcaption id=\"caption-attachment-41663\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 7. Constante diel\u00e9trica complexa<\/figcaption><\/figure>\r\n<figure id=\"attachment_41664\" aria-describedby=\"caption-attachment-41664\" style=\"width: 180px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41664\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/tan_delta.png\" alt=\"\" width=\"180\" height=\"75\" \/><figcaption id=\"caption-attachment-41664\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 8. Fator de dissipa\u00e7\u00e3o<\/figcaption><\/figure>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5&#8217; \u00e9 a parte real da constante diel\u00e9trica relativa do material;<\/span><\/li>\r\n<li class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5&#8221; \u00e9 a parte imagin\u00e1ria da constante diel\u00e9trica relativa do material;<\/span><\/li>\r\n<li class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b4 \u00e9 o \u00e2ngulo de perdas do material;<\/span><\/li>\r\n<li class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">tan(\u03b4) \u00e9 o fator de dissipa\u00e7\u00e3o do diel\u00e9trico;\u00a0<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<figure id=\"attachment_44381\" aria-describedby=\"caption-attachment-44381\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-44381 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/06\/dieletrico1.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/06\/dieletrico1.png 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/06\/dieletrico1-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/06\/dieletrico1-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-44381\" class=\"wp-caption-text\">Figura 2. Comportamento da constante diel\u00e9trica com a frequ\u00eancia.<\/figcaption><\/figure>\r\n<hr \/>\r\n<h3 id='exemplo-1-comportamento-da-\u00e1gua'  id=\"boomdevs_4\">Exemplo 1 &#8211; Comportamento da \u00e1gua<\/h3>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Figura 2 apresenta a Constante Diel\u00e9trica da \u00e1gua em fun\u00e7\u00e3o da frequ\u00eancia e da temperatura.<\/span><\/p>\r\n<p style=\"text-align: center;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 18pt;\">\n<div class=\"wdt-wrapper-chart-loader\" data-id=\"94\"\n     style=\"height: 600px;\">\n    <div class=\"wdt-main-item\">\n                <div class=\"wdt-chart-animated-background\" style=\"height: 150px\">\n            <div class=\"wdt-background-masker wdt-btn-divide-left wdt-chart-one\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-2\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-3\"><\/div>\n          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        container: \"wpDataChart_94\",\n            follow_filtering: 0,\n            wpdatatable_id: 166,\n            group_chart: 0        }\n    <\/script>\n\n    <div id=\"wpDataChart_94\" class=\"google_line_chart\" style=\"width: 100%\"><\/div>\n<\/span><\/p>\r\n<p style=\"text-align: center;\">\u00a0<span style=\"font-family: verdana, geneva, sans-serif; font-size: 12pt;\">Figura 2. Constante diel\u00e9trica da \u00e1gua.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Observa-se que at\u00e9 500 MHz, a constante diel\u00e9trica da \u00e1gua permanece constante e o fator de dissipa\u00e7\u00e3o praticamente nulo.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Contudo, a partir dos 500 MHz a componente real come\u00e7a a decrescer e a imagin\u00e1ria a aumentar independentemente da temperatura.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Al\u00e9m disso, a componente imagin\u00e1ria atinge um valor m\u00e1ximo entre 10 GHz e 30 GHz dependendo da temperatura. Ap\u00f3s essas frequ\u00eancias, ambas as componentes decrescem e tendem a zero.<\/span><\/p>\r\n<hr \/>\r\n<h2 id='exemplo-2-forno-de-micro-ondas'  id=\"boomdevs_5\"><span style=\"font-family: verdana, geneva, sans-serif;\">Exemplo 2 &#8211; Forno de Micro-ondas<\/span><\/h2>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">O forno de micro-ondas se tornou a aplica\u00e7\u00e3o pr\u00e1tica da constante diel\u00e9trica mais conhecida na vida moderna.<\/span><\/p>\r\n<p><a href=\"https:\/\/youtu.be\/bUsS5KUMLvw?si=s5EG9LSG24VbIAKu\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: verdana, geneva, sans-serif;\">A descoberta do Micro-0ndas<\/span><\/a><\/p>\r\n<p><a href=\"https:\/\/youtu.be\/D9_2qtD8flo?si=1UedGiVbXPH0DpG_\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: verdana, geneva, sans-serif;\">Forno de Micro-0ndas<\/span><\/a><\/p>\r\n<p><a href=\"https:\/\/youtu.be\/3JNQgdT8LWc?si=EbBdJ9BhK0vdkL1T\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: verdana, geneva, sans-serif;\">Magnetron<\/span><\/a><\/p>\r\n<hr \/>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Capacitores possuem maior utiliza\u00e7\u00e3o porque est\u00e3o presentes na maioria dos equipamentos el\u00e9tricos e eletr\u00f4nicos, mas se encontram invis\u00edveis ao p\u00fablico leigo.<\/span><\/p>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">O forno de micro-ondas consiste basicamente numa fonte de ondas eletromagn\u00e9ticas de frequ\u00eancia <span class=\"s1\">fi<\/span>xa (\u22cd2,4 GHz) que, ao se propagar atrav\u00e9s dos materiais diel\u00e9tricos, produz aquecimento.<\/span><\/p>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Todos sabem que n\u00e3o se deve colocar qualquer material no forno de micro-ondas, principalmente condutores.<\/span><\/p>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Al\u00e9m disso, alimentos diferentes se comportam de forma distinta no forno. Como explicar teoricamente este conhecimento emp\u00edrico?<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Figura 3 mostra uma micro-onda plana incidindo em determinado material homog\u00eaneo.<\/span><\/p>\r\n<figure id=\"attachment_41684\" aria-describedby=\"caption-attachment-41684\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41684 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/onda_plana.jpg\" alt=\"\" width=\"800\" height=\"640\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/onda_plana.jpg 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/onda_plana-300x240.jpg 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/onda_plana-768x614.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-41684\" class=\"wp-caption-text\">Figura 3. Micro-onda plana incidindo sobre um material<\/figcaption><\/figure>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Pode-se descrever o campo el\u00e9trico de uma onda eletromagn\u00e9tica plana e uniforme propagando em um material diel\u00e9trico homog\u00eaneo e isotr\u00f3pico da seguinte maneira:<\/span><\/p>\r\n<figure id=\"attachment_41668\" aria-describedby=\"caption-attachment-41668\" style=\"width: 753px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41668 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/micro-ondas_1.png\" alt=\"forno micro-ondas\" width=\"753\" height=\"293\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/micro-ondas_1.png 753w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/micro-ondas_1-300x117.png 300w\" sizes=\"(max-width: 753px) 100vw, 753px\" \/><figcaption id=\"caption-attachment-41668\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 9. Campo el\u00e9trico de uma onda eletromagn\u00e9tica plana num material diel\u00e9trico<\/figcaption><\/figure>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b1 \u00e9 o coeficiente de atenua\u00e7\u00e3o [1\/m];<\/span><\/li>\r\n<li class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b2 \u00e9 a coeficiente de fase [1\/m];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">t \u00e9 o tempo;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">z \u00e9 a dist\u00e2ncia percorrida pela onda no material;<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Ao penetrar no material a onda transfere energia para o material e, consequentemente, diminui de amplitude de forma exponencial.<\/span><\/p>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">O comprimento de onda &#8211; \u03bb &#8211; e a imped\u00e2ncia intr\u00ednseca &#8211; \u03b7 &#8211; ser\u00e3o dados por:<\/span><\/p>\r\n<figure id=\"attachment_41670\" aria-describedby=\"caption-attachment-41670\" style=\"width: 118px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41670 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/lambda.png\" alt=\"\" width=\"118\" height=\"86\" \/><figcaption id=\"caption-attachment-41670\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 10. Comprimento de onda<\/figcaption><\/figure>\r\n<figure id=\"attachment_41671\" aria-describedby=\"caption-attachment-41671\" style=\"width: 368px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41671 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/temp_8.png\" alt=\"\" width=\"368\" height=\"81\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/temp_8.png 368w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/temp_8-300x66.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><figcaption id=\"caption-attachment-41671\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 11. Imped\u00e2ncia intr\u00ednseca<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03bb \u00e9 o comprimento de onda;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b7 \u00e9 a imped\u00e2ncia intr\u00ednseca complexa[\u03a9];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b8<sub>n<\/sub> \u00e9 o \u00e2ngulo da imped\u00e2ncia intr\u00ednseca.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A imped\u00e2ncia intr\u00ednseca representa a imped\u00e2ncia do material vista pela onda.<\/span><\/p>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">A profundidade de penetra\u00e7\u00e3o, de<span class=\"s1\">fi<\/span>nida como sendo o inverso da constante de atenua\u00e7\u00e3o, representa a dist\u00e2ncia percorrida pela onda eletromagn\u00e9tica para que a amplitude do campo el\u00e9trico diminua 63% (1\/e).<\/span><\/p>\r\n<figure id=\"attachment_41674\" aria-describedby=\"caption-attachment-41674\" style=\"width: 112px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41674 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/dist_penetra.png\" alt=\"\" width=\"112\" height=\"134\" \/><figcaption id=\"caption-attachment-41674\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 12. Profundidade de penetra\u00e7\u00e3o<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b4<sub>p<\/sub> \u00e9 a profundidade de penetra\u00e7\u00e3o da onda;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b4<sub>pp<\/sub> \u00e9 a profundidade de dissipa\u00e7\u00e3o de pot\u00eancia da onda;<span id='easy-footnote-1-41645' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/#easy-footnote-bottom-1-41645\" title=\" ver equa\u00e7\u00e3o 13\"><sup>1<\/sup><\/a><\/span><\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Isto signi<span class=\"s1\">fi<\/span>ca que essa constante mede a capacidade de penetra\u00e7\u00e3o de determinada onda eletromagn\u00e9tica no material em quest\u00e3o.<\/span><\/p>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 13 apresenta a densidade de pot\u00eancia dissipada no material em fun\u00e7\u00e3o da imped\u00e2ncia intr\u00ednseca e do fator de atenua\u00e7\u00e3o do material. <span id='easy-footnote-2-41645' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/#easy-footnote-bottom-2-41645\" title=\" Equa\u00e7\u00e3o 9.96 da refer\u00eancia Notaros\"><sup>2<\/sup><\/a><\/span><\/span><\/p>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Neste caso, de<span class=\"s1\">fi<\/span>ne-se a profundidade de penetra\u00e7\u00e3o de pot\u00eancia como sendo a metade da profundidade de penetra\u00e7\u00e3o do campo el\u00e9trico em decorr\u00eancia do fator 2 no termo exponencial da Equa\u00e7\u00e3o 13.<\/span><\/p>\r\n<figure id=\"attachment_41673\" aria-describedby=\"caption-attachment-41673\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41673 size-medium\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/temp_9-300x81.png\" alt=\"\" width=\"300\" height=\"81\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/temp_9-300x81.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/temp_9.png 322w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-41673\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 13. Pot\u00eancia dissipada no material<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:\u00a0<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">p<sub>d<\/sub> \u00e9 a pot\u00eancia por comprimento dissipada no material;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">E<sub>xo<\/sub> \u00e9 a amplitude do campo el\u00e9trico da onda ao penetrar no material;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b7 \u00e9 a imped\u00e2ncia intr\u00ednseca complexa[\u03a9];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b8<sub>n<\/sub> \u00e9 o \u00e2ngulo da imped\u00e2ncia intr\u00ednseca.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b1 \u00e9 o coeficiente de atenua\u00e7\u00e3o [1\/m].<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Isto signi<span class=\"s1\">fi<\/span>ca que, dependendo da constante diel\u00e9trica do material e da frequ\u00eancia da onda eletromagn\u00e9tica, o aquecimento ocorrer\u00e1 de forma diferente.<\/span><\/p>\r\n<p>[wpdevart_youtube width=&#8221;640&#8243; height=&#8221;385&#8243; autoplay=&#8221;0&#8243; theme=&#8221;dark&#8221; loop_video=&#8221;0&#8243; enable_fullscreen=&#8221;1&#8243; show_related=&#8221;1&#8243; show_popup=&#8221;0&#8243; thumb_popup_width=&#8221;213&#8243; thumb_popup_height=&#8221;128&#8243; show_title=&#8221;1&#8243; show_youtube_icon=&#8221;1&#8243; show_annotations=&#8221;1&#8243; show_progress_bar_color=&#8221;white&#8221; autohide_parameters=&#8221;1&#8243; set_initial_volume=&#8221;true&#8221; initial_volume=&#8221;72&#8243; disable_keyboard=&#8221;1&#8243;]kp33ZprO0Ck[\/wpdevart_youtube]<\/p>\r\n<hr \/>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">As express\u00f5es anteriores relativas \u00e0 constante diel\u00e9trica consideraram os materiais isotr\u00f3picos. <\/span><\/p>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">No caso de materiais anisotr\u00f3picos, a constante diel\u00e9trica se transforma num tensor de acordo com a equa\u00e7\u00e3o 14.<\/span><\/p>\r\n<figure id=\"attachment_7551\" aria-describedby=\"caption-attachment-7551\" style=\"width: 418px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-7551 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2019\/06\/temp.png\" alt=\"\" width=\"418\" height=\"133\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2019\/06\/temp.png 418w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2019\/06\/temp-300x95.png 300w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><figcaption id=\"caption-attachment-7551\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 14. Constante diel\u00e9trica tensorial<\/figcaption><\/figure>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\"> Observa-se que a <b>Densidade de Fluxo El\u00e9trico <\/b>e a <b>Intensidade de Campo El\u00e9trico <\/b>s\u00e3o tensores de primeira ordem e, consequentemente, a <b>Constante Diel\u00e9trica <\/b>dos materiais \u00e9 um tensor de segunda ordem sim\u00e9trico com as seguintes peculiaridades:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">os elementos diagonais s\u00e3o positivos;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">os elementos fora da diagonal podem ser negativos;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">os elementos s\u00e3o n\u00fameros complexos;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">os elementos fora da diagonal possuem m\u00f3dulo menor do que os elementos da diagonal;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">os elementos variam com a frequ\u00eancia do campo el\u00e9trico;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">a parte imagin\u00e1ria se encontra associada \u00e0 perda de energia que ocorre no diel\u00e9trico;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">as partes real e imagin\u00e1ria da constante diel\u00e9trica podem ter comportamentos e simetrias distintos com a frequ\u00eancia.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">A simpli<span class=\"s1\">fi<\/span>ca\u00e7\u00e3o do tensor constante diel\u00e9trica depende da <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/arrumacao-dos-elementos-basicos\/sistemas-cristalinos-primitivos\/\">estrutura e da simetria<\/a> do material. A Tabela abaixo apresenta os diversos tipos de cristais existentes.<\/span><\/p>\r\n<h6 id='tabela-1-sistema-cristalinos'  id=\"boomdevs_6\" style=\"text-align: center;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 12pt;\">Tabela 1. Sistema Cristalinos<\/span><\/h6>\r\n<p style=\"text-align: center;\">\n<div class=\"wpdt-c wdt-skin-aqua\">\n    \n    <input type=\"hidden\" id=\"wdtNonceFrontendServerSide_40\" name=\"wdtNonceFrontendServerSide_40\" value=\"063f434246\" \/><input type=\"hidden\" name=\"_wp_http_referer\" value=\"\/blog\/wp-json\/wp\/v2\/pages\/41645\" \/><input type=\"hidden\" id=\"wdtFrontendelementorNonce_40\" name=\"wdtFrontendelementorNonce_40\" value=\"e35cb52665\" \/>    <input type=\"hidden\" id=\"table_2_desc\"\n           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   <table id=\"table_2\"\n           class=\" scroll responsive display nowrap wdt-no-display data-t data-t wpDataTable wpDataTableID-40 \"\n           style=\"\"\n           data-described-by='table_2_desc'\n           data-wpdatatable_id=\"40\">\n        \n        <!-- Table header -->\n        \n<thead>\n<tr>\n                    <th\n                        class=\" wdtheader sort numdata integer \"\n        style=\"\">        wdt_ID<\/th>        <th\n        data-class=\"expand\"                class=\" wdtheader sort \"\n        style=\"\">        Sistema<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        Restri\u00e7\u00f5es nas Dimens\u00f5es<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        Restri\u00e7\u00f5es nos \u00e2ngulos<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        Simetria M\u00e1xima<\/th>    <\/tr>\n<\/thead>\n        <!-- \/Table header -->\n\n        <!-- Table body -->\n        \n<tbody>\n<!-- Table body -->\n<div data-id=\"40\"\n     class=\"wdt-timeline-item wdt-timeline-table_2\"\n     style=\"\">\n    <div class=\"wdt-table-loader\">\n        <div class=\"wdt-table-loader-row wdt-table-loader-header\">\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n        <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n            <\/div>\n<\/div><!-- \/Table body -->\n                    <tr id=\"table_40_row_0\"\n            data-row-index=\"0\">\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">Tricl\u00ednico<\/td>\n                            <td style=\"\">nenhuma<\/td>\n                            <td style=\"\">nenhuma<\/td>\n                            <td style=\"\">\uffe31<\/td>\n                    <\/tr>\n                            <tr id=\"table_40_row_1\"\n            data-row-index=\"1\">\n                            <td style=\"\">2<\/td>\n                            <td style=\"\">Monocl\u00ednico<\/td>\n                            <td style=\"\">nenhuma<\/td>\n                            <td style=\"\">\u03b1=\u03b3=90\u00ba<\/td>\n                            <td style=\"\">2\/m<\/td>\n                    <\/tr>\n                            <tr id=\"table_40_row_2\"\n            data-row-index=\"2\">\n                            <td style=\"\">3<\/td>\n                            <td style=\"\">Ortorr\u00f4mbico<\/td>\n                            <td style=\"\">Nenhuma<\/td>\n                            <td style=\"\">\u03b1=\u03b2=\u03b3=90\u00ba<\/td>\n                            <td style=\"\">mmm<\/td>\n                    <\/tr>\n                            <tr id=\"table_40_row_3\"\n            data-row-index=\"3\">\n                            <td style=\"\">4<\/td>\n                            <td style=\"\">Tetragonal<\/td>\n                            <td style=\"\">a=b<\/td>\n                            <td style=\"\">\u03b1=\u03b2=\u03b3=90\u00ba<\/td>\n                            <td style=\"\">4\/mmm<\/td>\n                    <\/tr>\n                            <tr id=\"table_40_row_4\"\n            data-row-index=\"4\">\n                            <td style=\"\">5<\/td>\n                            <td style=\"\">Trigonal<\/td>\n                            <td style=\"\">a=b<\/td>\n                            <td style=\"\">\u03b1=\u03b2=90\u00ba, \u03b3=120\u00ba<\/td>\n                            <td style=\"\">\uffe33<\/td>\n                    <\/tr>\n                            <tr id=\"table_40_row_5\"\n            data-row-index=\"5\">\n                            <td style=\"\">6<\/td>\n                            <td style=\"\">Hexagonal<\/td>\n                            <td style=\"\">a=b<\/td>\n                            <td style=\"\">\u03b1=\u03b2=90\u00ba, \u03b3=120\u00ba<\/td>\n                            <td style=\"\">6\/mmm<\/td>\n                    <\/tr>\n                            <tr id=\"table_40_row_6\"\n            data-row-index=\"6\">\n                            <td style=\"\">7<\/td>\n                            <td style=\"\">C\u00fabico<\/td>\n                            <td style=\"\">a=b=c<\/td>\n                            <td style=\"\">\u03b1=\u03b2=\u03b3<\/td>\n                            <td style=\"\">m\uffe33m<\/td>\n                    <\/tr>\n            <\/tbody>        <!-- \/Table body -->\n\n        <!-- Table footer -->\n        \n        <!-- \/Table footer -->\n    <\/table>\n\n<\/div><style>\ntable.wpDataTable td.numdata { text-align: right !important; }\n<\/style>\n<style>\n                    \n                                                                                    .wpdt-c .wpDataTablesWrapper table.wpDataTable thead tr:nth-child(2) th {\n        overflow: visible;\n    }\n\n            \/* table font color *\/\n    .wpdt-c.wpDataTablesWrapper table.wpdtSimpleTable,\n    .wpdt-c .wpDataTablesWrapper table.wpDataTable {\n        font-family: Verdana, Geneva, sans-serif !important;\n    }\n\n            \/* table font size *\/\n    .wpdt-c.wpDataTablesWrapper table.wpdtSimpleTable,\n    .wpdt-c .wpDataTablesWrapper table.wpDataTable {\n        font-size: 24px !important;\n    }\n\n            \n                <\/style>\n<style>\n<\/style>\n<style>\n                            \n                                        \n                    \n<\/style>\n<\/p>\r\n<h2 id='materiais-tricl\u00ednicos'  id=\"boomdevs_7\" class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Materiais Tricl\u00ednicos<\/span><\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Para este tipo de materiais cristalinos, a Constante Diel\u00e9trica se torna um tensor completo conforme a Equa\u00e7\u00e3o 14.\u00a0<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O Carbonato de Calcio &#8211; CaCO<sub>3<\/sub> -, na forma de <a href=\"https:\/\/pt.wikipedia.org\/wiki\/Aragonita\" target=\"_blank\" rel=\"noopener\">Aragonita<\/a>, exemplifica este tipo de material. (\u03b5<sub>11<\/sub>=8,67, \u03b5<sub>22<\/sub>=8,69, e \u03b5<sub>33<\/sub>=8,31 @tamb @ 94GHz)<span id='easy-footnote-3-41645' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/#easy-footnote-bottom-3-41645\" title=\" CRC Handbook\"><sup>3<\/sup><\/a><\/span><\/span><\/p>\r\n<h2 id='materiais-monocl\u00ednicos'  id=\"boomdevs_8\"><span style=\"font-family: verdana, geneva, sans-serif;\">Materiais Monocl\u00ednicos<\/span><\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Materiais Monocl\u00ednicos possuem a constante diel\u00e9trica na forma do tensor da Figura 15. Os elementos da diagonal s\u00e3o distintos e apenas dois elementos fora da diagonal s\u00e3o diferentes de zero.<\/span><\/p>\r\n<figure id=\"attachment_41690\" aria-describedby=\"caption-attachment-41690\" style=\"width: 207px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41690 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/temp_2.png\" alt=\"\" width=\"207\" height=\"129\" \/><figcaption id=\"caption-attachment-41690\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 15. Tensor constante diel\u00e9trica de materiais monocl\u00ednicos<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A <a href=\"https:\/\/museuhe.com.br\/mineral\/gipsita-gypsum\/\" target=\"_blank\" rel=\"noopener\">Gipsita &#8211; Ca(SO<sub>4<\/sub>).2H<sub>2<\/sub>O<\/a> &#8211; exemplifica este tipo de material. (\u03b5<sub>11<\/sub>= 5,1, \u03b5<sub>22<\/sub>=5,24, \u03b5<sub>33<\/sub>= 10,30 @ tamb) <span id='easy-footnote-4-41645' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/#easy-footnote-bottom-4-41645\" title=\" CRC Handbook\"><sup>4<\/sup><\/a><\/span><\/span><\/p>\r\n<h2 id='materiais-ortorr\u00f4mbicos'  id=\"boomdevs_9\"><span style=\"font-family: verdana, geneva, sans-serif;\">Materiais Ortorr\u00f4mbicos<\/span><\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Materiais Ortorr\u00f4mbicos apresentam a constante diel\u00e9trica na forma do tensor da Figura 16. Os elementos da diagonal s\u00e3o distintos, mas todos os elementos fora da diagonal s\u00e3o nulos.<\/span><\/p>\r\n<figure id=\"attachment_41698\" aria-describedby=\"caption-attachment-41698\" style=\"width: 207px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41698 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/temp_3.png\" alt=\"\" width=\"207\" height=\"129\" \/><figcaption id=\"caption-attachment-41698\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 16. Tensor constante diel\u00e9trica de materiais ortorr\u00f4mbicos<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O <a href=\"https:\/\/museuhe.com.br\/mineral\/enxofre-sulphur\/\" target=\"_blank\" rel=\"noopener\">Enxofre<\/a> exemplifica esse tipo de material. (\u03b5<sub>11<\/sub>=3,75, \u03b5<sub>22<\/sub>=3,95, \u03b5<sub>33<\/sub>=4,44) <span id='easy-footnote-5-41645' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/#easy-footnote-bottom-5-41645\" title=\" CRC Handbook\"><sup>5<\/sup><\/a><\/span><\/span><\/p>\r\n<h2 id='materiais-uniaxiais'  id=\"boomdevs_10\"><span style=\"font-family: verdana, geneva, sans-serif;\">Materiais Uniaxiais<\/span><\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os materiais uniaxiais representam o conjunto formado pelos cristais Tetragonais, Trigonais e Hexagonais, e possuem a constante diel\u00e9trica na forma do tensor apresentado na Figura 17.\u00a0<\/span><\/p>\r\n<figure id=\"attachment_41719\" aria-describedby=\"caption-attachment-41719\" style=\"width: 205px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41719 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/temp_4.png\" alt=\"\" width=\"205\" height=\"129\" \/><figcaption id=\"caption-attachment-41719\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 17. Tensor constante diel\u00e9trica dos materiais uniaxiais<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O Titanato de B\u00e1rio &#8211; BaTiO3 &#8211; \u00e9 um exemplo desse tipo de material. (\u03b5<sub>11<\/sub>=3600, \u03b5<sub>33<\/sub>=150 sem press\u00e3o mec\u00e2nica @ 100 KHz, e \u03b5<sub>11<\/sub>=2300, \u03b5<sub>33<\/sub>=80 com press\u00e3o mec\u00e2nica @ 250MHz, todos @ 298 K) <span id='easy-footnote-6-41645' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/#easy-footnote-bottom-6-41645\" title=\" CRC Handbook\"><sup>6<\/sup><\/a><\/span><\/span><\/p>\r\n<h2 id='materiais-c\u00fabicos'  id=\"boomdevs_11\"><span style=\"font-family: verdana, geneva, sans-serif;\">Materiais C\u00fabicos<\/span><\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Finalmente, os materiais com cristais c\u00fabicos possuem apenas os elementos diagonais e s\u00e3o todos iguais. Isto significa que a nota\u00e7\u00e3o tensorial n\u00e3o se torna necess\u00e1ria com esses materiais.\u00a0<\/span><\/p>\r\n<figure id=\"attachment_41720\" aria-describedby=\"caption-attachment-41720\" style=\"width: 203px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41720 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/temp_5.png\" alt=\"\" width=\"203\" height=\"129\" \/><figcaption id=\"caption-attachment-41720\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 18. Tensor constante diel\u00e9trica dos materiais c\u00fabicos<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O \u00f3xido de cobre -CuO- exemplifica esse tipo de material (\u03b5 =18,1 @ tamb 2MHz) <span id='easy-footnote-7-41645' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/#easy-footnote-bottom-7-41645\" title=\" CRC Handbook\"><sup>7<\/sup><\/a><\/span><\/span><\/p>\r\n<h6 id='tabela-2-propriedades-diel\u00e9tricas'  id=\"boomdevs_12\" style=\"text-align: center;\"><span style=\"text-align: center; font-family: verdana, geneva, sans-serif;\">Tabela 2. Propriedades Diel\u00e9tricas <\/span><\/h6>\r\n<p style=\"text-align: center;\"><span style=\"text-align: center; font-family: verdana, geneva, sans-serif;\">\n<table id=\"tablepress-60\" class=\"tablepress tablepress-id-60\" aria-describedby=\"tablepress-60-description\">\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-1\">\n\t<td class=\"column-1\">Material<\/td><td class=\"column-2\">S\u00edmbolo<\/td><td class=\"column-3\">Rigidez Diel\u00e9trica[kV\/mm]<\/td><td class=\"column-4\">Constante Diel\u00e9trica Relativa<\/td><td class=\"column-5\">Observa\u00e7\u00f5es<\/td><td class=\"column-6\">Fator de dissipa\u00e7\u00e3o<\/td>\n<\/tr>\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Bromo<\/td><td class=\"column-2\">Br<\/td><td class=\"column-3\"><\/td><td class=\"column-4\">3,15<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td class=\"column-1\">Sel\u00eanio<\/td><td class=\"column-2\">Se<\/td><td class=\"column-3\"><\/td><td class=\"column-4\">6,60<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td class=\"column-1\">Alumina<\/td><td class=\"column-2\">Al2O3<\/td><td class=\"column-3\">9,00<\/td><td class=\"column-4\">9,3<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-5\">\n\t<td class=\"column-1\">Quartzo<\/td><td class=\"column-2\">SiO2<\/td><td class=\"column-3\"><\/td><td class=\"column-4\">4,2<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-6\">\n\t<td class=\"column-1\">Baquelite<\/td><td class=\"column-2\">Sumitomo Durez 22257<\/td><td class=\"column-3\">7,9<\/td><td class=\"column-4\">5,5<\/td><td class=\"column-5\">@ 1 MHz<\/td><td class=\"column-6\">0,08<\/td>\n<\/tr>\n<tr class=\"row-7\">\n\t<td class=\"column-1\">Germanium<\/td><td class=\"column-2\">Ge<\/td><td class=\"column-3\"><\/td><td class=\"column-4\">16<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-8\">\n\t<td class=\"column-1\">Sil\u00edcio<\/td><td class=\"column-2\">Si<\/td><td class=\"column-3\"><\/td><td class=\"column-4\">11,8<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-9\">\n\t<td class=\"column-1\">Estanho<\/td><td class=\"column-2\">Sn<\/td><td class=\"column-3\"><\/td><td class=\"column-4\">24<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-10\">\n\t<td class=\"column-1\">Metanol<\/td><td class=\"column-2\"><\/td><td class=\"column-3\"><\/td><td class=\"column-4\">32,63<br \/>\n<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-11\">\n\t<td class=\"column-1\">Etanol<\/td><td class=\"column-2\"><\/td><td class=\"column-3\"><\/td><td class=\"column-4\">24,3<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-12\">\n\t<td class=\"column-1\">PPA com fibra de vidro<\/td><td class=\"column-2\"><\/td><td class=\"column-3\">0.8 a 37,0<\/td><td class=\"column-4\">3,59 a 136<\/td><td class=\"column-5\">varia com a frequ\u00eancia e temperatura<\/td><td class=\"column-6\">0,005 a 0,85<\/td>\n<\/tr>\n<tr class=\"row-13\">\n\t<td class=\"column-1\">\u00c1gua<\/td><td class=\"column-2\">H2O<\/td><td class=\"column-3\"><\/td><td class=\"column-4\">55,51 a 87,9<br \/>\n80.2 @20C<\/td><td class=\"column-5\">varia com a temperatura e press\u00e3o<br \/>\n<\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-14\">\n\t<td class=\"column-1\">\u00c1gua Pesada<\/td><td class=\"column-2\">D2O<\/td><td class=\"column-3\"><\/td><td class=\"column-4\">78,06 @ 20C<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<tr class=\"row-15\">\n\t<td class=\"column-1\">Titanato de Bario<\/td><td class=\"column-2\">BaTiO3<\/td><td class=\"column-3\"><\/td><td class=\"column-4\">1000 a 5000<\/td><td class=\"column-5\"><\/td><td class=\"column-6\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<span id=\"tablepress-60-description\" class=\"tablepress-table-description tablepress-table-description-id-60\">Fonte: Matweb<\/span>\n<!-- #tablepress-60 from cache --><\/span><\/p>\r\n<h2 id='modelo-equivalente'  id=\"boomdevs_13\"><span style=\"font-family: verdana, geneva, sans-serif;\">Modelo Equivalente\u00a0<\/span><\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Para analisar circuitos el\u00e9tricos com materiais diel\u00e9tricos, pode-se utilizar as seguintes express\u00f5es:<\/span><\/p>\r\n<figure id=\"attachment_41722\" aria-describedby=\"caption-attachment-41722\" style=\"width: 262px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"size-full wp-image-41722\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/modelo_capacitor.png\" alt=\"\" width=\"262\" height=\"181\" \/><figcaption id=\"caption-attachment-41722\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 19. Modelo do Capacitor<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde: <\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">C \u00e9 a capacit\u00e2ncia equivalente;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">C<sub>0<\/sub> \u00e9 a capacit\u00e2ncia sem o material diel\u00e9trico;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">R \u00e9 a resist\u00eancia equivalente em paralelo com o capacitor;<\/span><\/li>\r\n<li class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5&#8217; \u00e9 a parte real da constante diel\u00e9trica relativa do material;<\/span><\/li>\r\n<li class=\"p2\"><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5&#8221; \u00e9 a parte imagin\u00e1ria da constante diel\u00e9trica relativa do material;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c9 \u00e9 a frequ\u00eancia da tens\u00e3o\/corrente aplicada no material.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<hr \/>\r\n<h2 id='exemplo-3-material-diel\u00e9trico-entre-duas-placas-paralelas'  id=\"boomdevs_14\">Exemplo 3 &#8211; Material diel\u00e9trico entre duas placas paralelas<\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por exemplo, considerando um material diel\u00e9trico capacitor de placas paralelas, conforme mostra a Figura 4, C<sub>0<\/sub> possuir\u00e1 o valor apresentado na Equa\u00e7\u00e3o 20.<span id='easy-footnote-8-41645' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/#easy-footnote-bottom-8-41645\" title=\" Capacitor de placas paralelas\"><sup>8<\/sup><\/a><\/span><\/span><\/p>\r\n<p>&nbsp;<\/p>\r\n<figure id=\"attachment_41724\" aria-describedby=\"caption-attachment-41724\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41724 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/capacitor.jpg\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/capacitor.jpg 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/capacitor-300x225.jpg 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/capacitor-768x576.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-41724\" class=\"wp-caption-text\">Figura 4. Diel\u00e9trico entre placas paralelas<\/figcaption><\/figure>\r\n<figure id=\"attachment_41733\" aria-describedby=\"caption-attachment-41733\" style=\"width: 199px\" class=\"wp-caption alignnone\"><img decoding=\"async\" class=\"size-full wp-image-41733\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/C_placa_para.png\" alt=\"\" width=\"199\" height=\"88\" \/><figcaption id=\"caption-attachment-41733\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 20. Capacit\u00e2ncia de placas paralelas no v\u00e1cuo<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Figura 5 apresenta o circuito equivalente de materiais diel\u00e9tricos submetidos a campos el\u00e9tricos.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">\u00c9 importante observar que este modelo se mant\u00e9m v\u00e1lido para qualquer geometria porque o efeito da geometria se encontra no c\u00e1lculo de C<sub>0<\/sub>.<\/span><\/p>\r\n<figure id=\"attachment_41738\" aria-describedby=\"caption-attachment-41738\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-41738 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/capaci_P_Para1.jpg\" alt=\"\" width=\"800\" height=\"640\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/capaci_P_Para1.jpg 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/capaci_P_Para1-300x240.jpg 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/capaci_P_Para1-768x614.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-41738\" class=\"wp-caption-text\">Figura 5. Modelo equivalente do diel\u00e9trico<\/figcaption><\/figure>\r\n<h5 id='refer\u00eancias'  id=\"boomdevs_15\"><span style=\"font-family: verdana, geneva, sans-serif;\">Refer\u00eancias<\/span><\/h5>\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">AGILENT TECHNOLOGIES, <strong>Basics of Measuring the Dielectrics Properties of Materials \u2013 Application Note,<\/strong><\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">HAYNES, W.M., LIDE, D.\u00a0 R., BRUNO, T. J., (editors) <strong>Handbook of Chemistry and Physics<\/strong>, CRC Press, 93 ed., 2013.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">KAO, K.C.,\u00a0<strong>Dielectric Phenomena in Solids<\/strong>, Elsevier, 2004.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">NOTAROS, B. M., <strong>Eletromagnetismo<\/strong>, Pearson, 2012. <span id='easy-footnote-9-41645' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/#easy-footnote-bottom-9-41645\" title=\" kindle\"><sup>9<\/sup><\/a><\/span><\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">PEEK, F. W.,\u00a0<strong>Dielectric Phenomena in High Voltage Engineering<\/strong>, McGraw-Hill, 2 ed., 1920.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">RAJU, G. G.,\u00a0<strong>Dielectrics in Electric Fields<\/strong>, Dekker, 2002.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">SOLYMAR, L., WALSH, D., SYMS, R. R. A., <strong>Electrical Properties of Materials<\/strong>, Oxford, 10 ed., 2019. <span id='easy-footnote-10-41645' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/constante-dieletrica\/#easy-footnote-bottom-10-41645\" title=\"kindle\"><sup>10<\/sup><\/a><\/span><\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">VON HIPPEL, A. R.,\u00a0<strong>Dielectrics and Waves<\/strong>, MIT, 1954.<\/span><\/li>\r\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>Introdu\u00e7\u00e3o A Constante Diel\u00e9trica ou Permissividade El\u00e9trica Relativa -\u03b5r&#8211; consiste na capacidade do material de armazenar cargas el\u00e9tricas e traduz, de forma macrosc\u00f3pica, os efeitos que ocorrem no interior de \u00e1tomos e mol\u00e9culas devido ao campo el\u00e9trico. Portanto, ela se encontra diretamente relacionada \u00e0 estrutura da mat\u00e9ria, e varia em mais de 4 ordens de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":41496,"parent":2385,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"templates\/template-full-width.php","meta":{"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-41645","page","type-page","status-publish","has-post-thumbnail","hentry"],"uagb_featured_image_src":{"full":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/isolantes.jpg",1200,280,false],"thumbnail":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/isolantes-150x150.jpg",150,150,true],"medium":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/isolantes-300x70.jpg",300,70,true],"medium_large":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/isolantes-768x179.jpg",580,135,true],"large":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/isolantes-1024x239.jpg",580,135,true],"1536x1536":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/isolantes.jpg",1200,280,false],"2048x2048":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/isolantes.jpg",1200,280,false],"post-thumbnail":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/isolantes.jpg",1200,280,false],"twentytwenty-fullscreen":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/10\/isolantes.jpg",1200,280,false]},"uagb_author_info":{"display_name":"admin","author_link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/author\/admin\/"},"uagb_comment_info":0,"uagb_excerpt":"Introdu\u00e7\u00e3o A Constante Diel\u00e9trica ou Permissividade El\u00e9trica Relativa -\u03b5r&#8211; consiste na capacidade do material de armazenar cargas el\u00e9tricas e traduz, de forma macrosc\u00f3pica, os efeitos que ocorrem no interior de \u00e1tomos e mol\u00e9culas devido ao campo el\u00e9trico. Portanto, ela se encontra diretamente relacionada \u00e0 estrutura da mat\u00e9ria, e varia em mais de 4 ordens de&hellip;","_links":{"self":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/41645","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/comments?post=41645"}],"version-history":[{"count":81,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/41645\/revisions"}],"predecessor-version":[{"id":45261,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/41645\/revisions\/45261"}],"up":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/2385"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/media\/41496"}],"wp:attachment":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/media?parent=41645"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}