tag:blogger.com,1999:blog-28133305738403028612024-02-07T18:55:21.014+06:00Field and Wave ElectromagneticsInto physics, electron magnetic radiation refers to the waves of the electromagnetic field. It includes radio waves, microwaves, infrared, light, ultraviolet, X-rays, and gamma rays.Unknownnoreply@blogger.comBlogger14125tag:blogger.com,1999:blog-2813330573840302861.post-16311485393438069742010-01-16T17:51:00.000+06:002017-11-02T14:28:21.846+06:00Equation of Continunity<div dir="ltr" style="text-align: left;" trbidi="on">
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-15983934511942917512010-01-16T17:44:00.000+06:002017-11-02T14:52:37.968+06:00Farady's Law of Electromagnetic Induction<div dir="ltr" style="text-align: left;" trbidi="on">
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLTkiIGNPqcNmtYIKjIXwQ225iuFYj-u1z6uqeF1tUMz9qq37ZjKd_n7KyuZEJRuEZQVfg81v83MRnYMu-WBb1O2a8cwbeIjt292PtyL2u8l3Ayl-YiZJIFfjwXIl2KGF30F-BaXYdynA/s1600-h/1.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5427303315055205426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLTkiIGNPqcNmtYIKjIXwQ225iuFYj-u1z6uqeF1tUMz9qq37ZjKd_n7KyuZEJRuEZQVfg81v83MRnYMu-WBb1O2a8cwbeIjt292PtyL2u8l3Ayl-YiZJIFfjwXIl2KGF30F-BaXYdynA/s1600/1.JPG" style="float: left; margin: 0pt 10px 10px 0pt;" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Farady's Law of Electromagnetic Induction</td></tr>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-49389703428583447792010-01-16T17:25:00.000+06:002010-01-16T17:44:14.512+06:00The Significance of Displacement Current<meta equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 10"><meta name="Originator" content="Microsoft Word 10"><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:donotshowrevisions/> <w:donotprintrevisions/> <w:donotshowmarkup/> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><style> <!-- /* Font Definitions */ @font-face {font-family:"Angsana New"; panose-1:2 2 6 3 5 4 5 2 3 4; mso-font-charset:222; mso-generic-font-family:roman; mso-font-format:other; mso-font-pitch:variable; mso-font-signature:16777217 0 0 0 65536 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; mso-bidi-font-size:14.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Angsana New"; mso-bidi-language:TH;} @page Section1 {size:595.3pt 841.9pt; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:35.4pt; mso-footer-margin:35.4pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> </style><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--><div style="text-align: justify;">The Ampere’s Circuital Law for static field is no longer useful in time varying fields as is shown below: </div><p style="text-align: justify;" class="MsoNormal">Taking the divergence of the Ampere’s Circuital Law give by <span style="">▼×<b style="">H = J</b></span> and using the continuity equation we have</p><p style="text-align: justify;" class="MsoNormal"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiRobSEVI85iHEBVm63PBtnTovnqQUfQsw5fMzveifR9Kr8Rnc2cJ42PKnKImVoeFT8LkAbo3JJHkcgeCAJVVJ3WmesK6WOk5IBhW90aERTVk1kpGa6UnBBZwq3B0Jx2xlQOhQGwC7wEU/s1600-h/1.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 185px; height: 85px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiRobSEVI85iHEBVm63PBtnTovnqQUfQsw5fMzveifR9Kr8Rnc2cJ42PKnKImVoeFT8LkAbo3JJHkcgeCAJVVJ3WmesK6WOk5IBhW90aERTVk1kpGa6UnBBZwq3B0Jx2xlQOhQGwC7wEU/s400/1.JPG" alt="" id="BLOGGER_PHOTO_ID_5427300233874174226" border="0" /></a></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal">
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<br /></p><p style="text-align: justify;" class="MsoNormal">That is, equation <span style="">▼×<b style="">H = J</b></span> leads to steady state conditions in which charge density is not time varying function. Therefore, for time dependent fields’ <span style="">▼×<b style="">H = J</b></span> needs some modifications. Maxwell suggested that the definition of total current density of Ampere’s Circuital Law is incomplete and advised to add something to<b style=""><span style=""> J</span></b>. If it is assumed to be <b style=""><span style="">J’</span></b>, we have</p><p style="text-align: justify;" class="MsoNormal"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiztPrlNAAQ81dxVZTWvSPRkaF6V3P6MB0MQteE1fGXOVbZ8xFgIXwGc6ip2PmvCUk4sM6DvHKAnm76heX1CmZ2qIKXsh0V7Vo6zBoVqZs0vs3ZJ0u4Rdv5cXl-_6idfEd8PBbPpo3F9qw/s1600-h/2.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 181px; height: 216px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiztPrlNAAQ81dxVZTWvSPRkaF6V3P6MB0MQteE1fGXOVbZ8xFgIXwGc6ip2PmvCUk4sM6DvHKAnm76heX1CmZ2qIKXsh0V7Vo6zBoVqZs0vs3ZJ0u4Rdv5cXl-_6idfEd8PBbPpo3F9qw/s400/2.JPG" alt="" id="BLOGGER_PHOTO_ID_5427300238643891858" border="0" /></a></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal">
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<br /></p><p style="text-align: justify;" class="MsoNormal">Since <b style=""><span style="">J’</span></b> arises due to the variation of electric displacement (electric flux density) <b style="">D</b> with time, it is termed as displacement current density. The modified Ampere’s Circuital Law (Maxwell’s equation), therefore, for time varying field takes the following form</p><p style="text-align: justify;" class="MsoNormal"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDPs4VSvVZWStlylzGgetetKBrQI8hLCVeE0EMxHEqx-D7EkRpyL8dWdD0NCXl1R-guSp2Krty-4cfSkSASD07aNyGPu7HuRlL4j4Qsu7HJUqZXIu5P8rZFZDd-8WvakuI2O704MvUUbQ/s1600-h/3.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 175px; height: 44px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDPs4VSvVZWStlylzGgetetKBrQI8hLCVeE0EMxHEqx-D7EkRpyL8dWdD0NCXl1R-guSp2Krty-4cfSkSASD07aNyGPu7HuRlL4j4Qsu7HJUqZXIu5P8rZFZDd-8WvakuI2O704MvUUbQ/s400/3.JPG" alt="" id="BLOGGER_PHOTO_ID_5427300242402838626" border="0" /></a></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal">
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<br /></p><p style="text-align: justify;" class="MsoNormal">Applying Stokes’s Theorem in equation (1) can be given in integral form as<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1VfyYEK7uXQRCy4M4LHCDtaYoXO2bnLLsKvLeT3y2yKSIvo6TdOXXUm13qodSBs5nw9gK7HE7t9zsfnehCBjTukKJSKh9NRBK6b04OR6GDH0xfNCaklmvJ9qcUJsH81ng_RoZ1GHLUi0/s1600-h/4.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 343px; height: 51px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1VfyYEK7uXQRCy4M4LHCDtaYoXO2bnLLsKvLeT3y2yKSIvo6TdOXXUm13qodSBs5nw9gK7HE7t9zsfnehCBjTukKJSKh9NRBK6b04OR6GDH0xfNCaklmvJ9qcUJsH81ng_RoZ1GHLUi0/s400/4.JPG" alt="" id="BLOGGER_PHOTO_ID_5427300246943124802" border="0" /></a></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal">
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<br /></p><p style="text-align: justify;" class="MsoNormal">The important conclusion that can be drawn now is that, since displacement current is related to the electric field, it is not possible in case of time varying fields to deal separately with electric and magnetic fields but, instead, the two fields are interlinked giving rise to electromagnetic fields. It is to be noted that, in a good conductor <b style="">J’</b> is negligible compared to <b style="">J</b> at frequency lower than light frequencies (10<sup>15</sup> Hz).</p> Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-75056394320157182882010-01-16T17:11:00.001+06:002017-11-02T14:37:01.756+06:00Maxwell's Equations and their Physical Significances<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-size: 100%;">By studying the physical properties of electric (<b>E</b>-field) and magnetic (<b>B</b>-field) fields we have been able to describe these properties by four, relatively simple, equations known as Maxwell’s equations. </span></div>
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These four fundamental equations of electromagnetism can be expressed in both an integral and differential form as tabulated below:</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8PeVjmK35QFnWCM21SO6_5RN5adpbJMwecqgpeLZ0rReh0PKu-nzNkWR1ywGb69QNB0hFmSWjSSo0XNXFoG9GD_26J64uWajgNteLTfyg8ghKOJLrreuhCb-7SmV-P82sqDt5gcYewlc/s1600-h/1.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5427295899436363698" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8PeVjmK35QFnWCM21SO6_5RN5adpbJMwecqgpeLZ0rReh0PKu-nzNkWR1ywGb69QNB0hFmSWjSSo0XNXFoG9GD_26J64uWajgNteLTfyg8ghKOJLrreuhCb-7SmV-P82sqDt5gcYewlc/s1600/1.JPG" style="float: left; margin: 0pt 10px 10px 0pt;" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small; text-align: justify;">Coulomb’s and Gauss’s Laws</span></td></tr>
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Equation (1) results from Coulomb’s and Gauss’s Laws and states that free charges act as sources or sinks of <b>D</b>. It suggests that the total electric flux density or total electric displacement through the surface enclosing a volume v is equal to the total charge within the volume.</div>
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Equation (2) arises from the application of Gauss’s law to magnetic fields and the non-existence of magnetic monopoles. There are no sources or sinks of <b>B</b>. This equation suggests that the net magnetic flux emerging through any closed surface is zero.</div>
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Equation (3) describes Faraday’s Law of electromagnetic induction and states that an electromotance is produced in a circuit when the magnetic flux through the circuit changes. It suggests that the electromagnetic force around a closed path is equal to the time derivative of the magnetic flux density through any surface bounded by the path.</div>
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Equation (4) describes Ampere’s Circuital Law (which is derived from the Biot-Savart Law) and states that the electromotive force around a closed path is equal to the conduction current J = σ<b>E</b> plus the time derivative of the electric flux density through any surface bounded by the path.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibviB6RXv6z0VNG4AGjV68iRmgqd2JMkXUCx3OJ8jQRSyCpPuMIWR5iI1HVWKNEBnSu4LrjyPCejwGciB3jNwRTfgBpZExfGLaDn3AxizJRGhQtCPHiFPOddlob_8a31uGaWpm3wZlGAM/s1600-h/2.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5427296232282133394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibviB6RXv6z0VNG4AGjV68iRmgqd2JMkXUCx3OJ8jQRSyCpPuMIWR5iI1HVWKNEBnSu4LrjyPCejwGciB3jNwRTfgBpZExfGLaDn3AxizJRGhQtCPHiFPOddlob_8a31uGaWpm3wZlGAM/s1600/2.JPG" style="float: left; margin: 0pt 10px 10px 0pt;" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Maxwell’s equations</td></tr>
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In vacuum/free space ρ<sub>v</sub> = 0<!--[if supportFields]><span style="'mso-element:field-begin'"></span> EQ <![endif]--><!--[if supportFields]><span style="'mso-element:field-end'"></span><![endif]-->, J = 0, ε = ε<sub>o</sub> and μ = μ<sub>o</sub>. Therefore, in vacuum the Maxwell’s equations take the following forms: </div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-44582869783354700682010-01-16T17:07:00.001+06:002017-11-02T14:38:10.621+06:00Maxwell's Equations in Frequency Domain<div dir="ltr" style="text-align: left;" trbidi="on">
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Assuming the fields are varying harmonically with time as e<sup>j</sup><sup>ωt</sup>, the Maxwell’s equations are given by<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
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<tr><td class="tr-caption" style="text-align: center;">Maxwell’s equations</td></tr>
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-63962190264416081822010-01-16T16:55:00.000+06:002017-11-02T14:41:06.171+06:00Maxwell's Equations in Phasor Form<div dir="ltr" style="text-align: left;" trbidi="on">
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In case the field quantities are sinusoidally time varying; the electric field <b>E</b> can be expressed as </div>
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<b>E</b>(x, y, z, t) = E<sub>x</sub> (x, y, z, t)<b>a<sub>x</sub></b> +E<sub>y</sub> (x, y , z, t) <b>a<sub>y</sub></b> + E<sub>z</sub> (x, y, z, t) <b>a<sub>z</sub></b></div>
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Where E<sub>x</sub> = E<sub>xm</sub> cos(ωt+θ<sub>x</sub>), E<sub>y</sub> = E<sub>ym</sub> cos(ωt+θ<sub>y</sub>), E<sub>z</sub> = E<sub>zm</sub> cos (ωt+θ<sub>z</sub>). Here the magnitudes E<sub>xm</sub>, E<sub>ym</sub>, E<sub>zm</sub>, and the phase angles θ<sub>x</sub>, θ<sub>y</sub>, θ<sub>z</sub>, are independent of time but may depend on spatial coordinates, e. g., E<sub>xm</sub> (x, y, z), θ<sub>x</sub>(x, y, z). Now E<sub>x</sub> can be expressed as</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvQQWDs6Rx8I4q9mDEf98mhzzSvhMz3hH0eWPcvR8Wz3jTnf3_Tf-Hg4DMs4VcsSUnBwzpKWVFDkpzqqH85paLcQGBHFr4sfXkvt6sbYSmX5sEViJX6YjTS_0FvDYmp0FeDMJcS7k8zcw/s1600-h/1.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5427290753717977090" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvQQWDs6Rx8I4q9mDEf98mhzzSvhMz3hH0eWPcvR8Wz3jTnf3_Tf-Hg4DMs4VcsSUnBwzpKWVFDkpzqqH85paLcQGBHFr4sfXkvt6sbYSmX5sEViJX6YjTS_0FvDYmp0FeDMJcS7k8zcw/s1600/1.JPG" style="float: left; margin: 0pt 10px 10px 0pt;" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Maxwell's Equations<br /></td></tr>
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<span style="font-size: 12.8px; text-align: center;">That is, the first derivative of a sinusoidal varying field is j</span><span style="text-align: justify;">ω</span><span style="text-align: justify;"> times the field. Therefore, the Maxwell’s equations in phasor form can be expressed as:</span><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7ouU9fHIjH2uVg_aAhN_hQJvVmld08V1EZfHxG1pFRD_pw5a0MurystPmNcEa_7PhQuWnWSegAG7Xqvs4dBswiPtOroxRg_JfDMF9lkUSHjgCxvIzIg0kqNVb9bHGQi7-GBYCYMhKeU0/s1600-h/2.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5427291326279976178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7ouU9fHIjH2uVg_aAhN_hQJvVmld08V1EZfHxG1pFRD_pw5a0MurystPmNcEa_7PhQuWnWSegAG7Xqvs4dBswiPtOroxRg_JfDMF9lkUSHjgCxvIzIg0kqNVb9bHGQi7-GBYCYMhKeU0/s400/2.JPG" style="float: left; height: 163px; margin: 0pt 10px 10px 0pt; width: 376px;" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Maxwell's Equations in Phasor Form</td></tr>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-40305955644768358752010-01-16T16:51:00.000+06:002017-11-02T14:41:48.069+06:00Faraday’s Law for time varying field<div dir="ltr" style="text-align: left;" trbidi="on">
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLvvMV_vjRWB-xIU8DFdG9qoN5ptuFbUQQy63sMlhz_4VDydi0Ceq6LxcFDgNEHWXefU5YV61yMRTTQxlp52oAUrkfN7n3aZ2-7oseVG-Ccs9Jrp7nZ2VZAWC55yJ6bt9rtsVJ3Kknzzc/s1600-h/1.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5427289374481398162" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLvvMV_vjRWB-xIU8DFdG9qoN5ptuFbUQQy63sMlhz_4VDydi0Ceq6LxcFDgNEHWXefU5YV61yMRTTQxlp52oAUrkfN7n3aZ2-7oseVG-Ccs9Jrp7nZ2VZAWC55yJ6bt9rtsVJ3Kknzzc/s400/1.JPG" style="float: left; height: 158px; margin: 0pt 10px 10px 0pt; width: 376px;" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Faraday’s Law for time varying field</td></tr>
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</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-45642864807396115212010-01-16T16:30:00.000+06:002017-11-02T14:47:28.578+06:00Electromagnetic Wave Equation or Helmholtz Equation<div dir="ltr" style="text-align: left;" trbidi="on">
<!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><style> <!-- /* Font Definitions */ @font-face {font-family:"Angsana New"; panose-1:2 2 6 3 5 4 5 2 3 4; mso-font-charset:222; mso-generic-font-family:roman; mso-font-format:other; mso-font-pitch:variable; mso-font-signature:16777217 0 0 0 65536 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; mso-bidi-font-size:14.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Angsana New"; mso-bidi-language:TH;} @page Section1 {size:8.5in 11.0in; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:.5in; mso-footer-margin:.5in; mso-paper-source:0;} div.Section1 {page:Section1;} </style> <br />
<span style="text-align: justify;">We will consider a linear, isotropic, homogeneous medium. Moreover, the net free charge in the source free region is zero (ρ</span><sub style="text-align: justify;">v</sub><span style="text-align: justify;"> = 0) and that any currents in the region are conduction currents (</span><b style="text-align: justify;">J</b><span style="text-align: justify;">=σ</span><b style="text-align: justify;">E</b><span style="text-align: justify;">). These types of regions are quite general ones and include the practical cases of free space (σ = 0) as well as most conductors and dielectrics. Maxwell’s equations for this region:</span><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNyPbg8hRKWMfNIYhABt44IrCeKqk5MwuaAKI6weA7pxsYxiwtcaOKHtZbLxWumASKaEybirIj_NWZDztIlIVbKvttN0-trm__Wa3ihO7rB1cH3i_o1UY7D2iRYGKnYb-eJ6KbmLnMGbk/s1600-h/1.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5427286032778618658" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNyPbg8hRKWMfNIYhABt44IrCeKqk5MwuaAKI6weA7pxsYxiwtcaOKHtZbLxWumASKaEybirIj_NWZDztIlIVbKvttN0-trm__Wa3ihO7rB1cH3i_o1UY7D2iRYGKnYb-eJ6KbmLnMGbk/s1600/1.JPG" style="float: left; margin: 0pt 10px 10px 0pt;" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Electromagnetic Wave Equation<br /></td></tr>
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<div class="MsoNormal" style="text-align: justify;">
<span style="text-align: left;">Taking curl of (3) and substituting (1) and (4) we have</span><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvSvQoG4c7lcpvvGZ_dDMB-d2jJNuWxQepo2biB2wI-Y7APg2SiZVW03UTMjm6UWVqECXSDuNyoz9rXSs9Yo1qeZ59IduRchYrpTsKyaMyWXlcAGRDWS8QEip6to4dZtPig_0Ms9flx40/s1600-h/3.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5427286023990175698" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvSvQoG4c7lcpvvGZ_dDMB-d2jJNuWxQepo2biB2wI-Y7APg2SiZVW03UTMjm6UWVqECXSDuNyoz9rXSs9Yo1qeZ59IduRchYrpTsKyaMyWXlcAGRDWS8QEip6to4dZtPig_0Ms9flx40/s1600/3.JPG" style="float: left; margin: 0pt 10px 10px 0pt;" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small; text-align: justify;">Taking </span>Curl</td></tr>
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<br /></div>
<div class="MsoNormal">
Similarly, by taking curl of (4) and substituting (2) and (3) we have</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIBethisJsucM58H8voGznWbV8yOQIEzJuSwsxjX3rk4fd2678k9kPowEUpVpcTBpbpQOfUpP-gqsrYI7KAVehHgfhTwJDAVKwAnmy_Vgoi1z4nYtf4Y6q0-KLOWS57z-0K3-R_-7ww9c/s1600-h/2.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5427286027635107202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIBethisJsucM58H8voGznWbV8yOQIEzJuSwsxjX3rk4fd2678k9kPowEUpVpcTBpbpQOfUpP-gqsrYI7KAVehHgfhTwJDAVKwAnmy_Vgoi1z4nYtf4Y6q0-KLOWS57z-0K3-R_-7ww9c/s1600/2.JPG" style="float: left; margin: 0pt 10px 10px 0pt;" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Taking <span style="font-size: 12.8px;">Curl<br /></span></td></tr>
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The equations in (5) are called electromagnetic wave equations or Helmholtz equations. Equations (5a) and (5c) are given in time domain and equations (5b) and (5 d) are in terms of the phasor form. The wave equations in <b>E</b> and in <b>H</b> have exactly the same form.<br />
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Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-2813330573840302861.post-57090977571510627362010-01-16T16:24:00.000+06:002010-01-16T16:29:51.814+06:00Characteeristics of a Uniform Plane Wave<div style="text-align: justify;"><meta equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 10"><meta name="Originator" content="Microsoft Word 10"><link rel="File-List" href="file:///C:%5CDOCUME%7E1%5CRashad%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml"><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><style> <!-- /* Font Definitions */ @font-face {font-family:"Angsana New"; panose-1:2 2 6 3 5 4 5 2 3 4; mso-font-charset:222; mso-generic-font-family:roman; mso-font-format:other; mso-font-pitch:variable; mso-font-signature:16777217 0 0 0 65536 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; mso-bidi-font-size:14.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Angsana New"; mso-bidi-language:TH;} @page Section1 {size:595.3pt 841.9pt; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:35.4pt; mso-footer-margin:35.4pt; mso-paper-source:0;} div.Section1 {page:Section1;} /* List Definitions */ @list l0 {mso-list-id:293485445; mso-list-type:hybrid; mso-list-template-ids:472184658 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;} @list l0:level1 {mso-level-tab-stop:.5in; mso-level-number-position:left; text-indent:-.25in;} ol {margin-bottom:0in;} ul {margin-bottom:0in;} --> </style><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--> </div><p style="text-align: justify;" class="MsoNormal"><span style="font-size:130%;">Uniform plan waves satisfy the following conditions:<o:p></o:p></span></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 0.5in; text-indent: -0.25in; text-align: justify;"><!--[if !supportLists]--><span style="font-size:130%;"><span style="">1.<span style=";font-family:";" > </span></span>At every point in space E and H are perpendicular to each other and to the direction of propagation. No fields, therefore, in the direction of wave propagation.<o:p></o:p></span><!--[endif]--></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 0.5in; text-indent: -0.25in; text-align: justify;"><!--[if !supportLists]--><span style="font-size:130%;"><span style="">2.<span style=";font-family:";" > </span></span>Everywhere in space, the fields vary harmonically with time and at the same frequency.<o:p></o:p></span><!--[endif]--></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 0.5in; text-indent: -0.25in; text-align: justify;"><!--[if !supportLists]--><span style="font-size:130%;"><span style="">3.<span style=";font-family:";" > </span></span>Each field has the same direction, magnitude and phase at every point in any plane perpendicular to the direction of wave propagation. The fields, therefore, are only function of the coordinate that represents the direction of wave propagation.<o:p></o:p></span><!--[endif]--></p> Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-73149605231152964122010-01-16T16:14:00.000+06:002017-11-02T14:51:19.617+06:00Field Equations of a Uniform Plane Wave<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAE81MuAoXHs8F2NzulZrXiOsDr9tqDaXildat4V6UFEje7AYWQFLoVGD02pn86cWPscgXFTVkKtdVSRE6udQG8AhTSyf8h4bC0nBUlIRQqkBwKmusTGKpTpClC3OFBHEJ-FPff8PnuiU/s1600-h/Field+Equations+of+a+Uniform+Plane+Wave+1.JPG" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img alt="" border="0" height="305" id="BLOGGER_PHOTO_ID_5427281399499700978" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAE81MuAoXHs8F2NzulZrXiOsDr9tqDaXildat4V6UFEje7AYWQFLoVGD02pn86cWPscgXFTVkKtdVSRE6udQG8AhTSyf8h4bC0nBUlIRQqkBwKmusTGKpTpClC3OFBHEJ-FPff8PnuiU/s400/Field+Equations+of+a+Uniform+Plane+Wave+1.JPG" style="float: center; margin: 0pt 10px 10px 0pt;" width="400" /></a><br />
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-22193133187224777332010-01-16T16:13:00.000+06:002010-01-16T16:14:30.308+06:00Propagation Constant and Intrinsic Impedance of Lossless Media<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgj1-ztZ3sZ5EMgTUAc8NvHz6V4hJYdiG7iIeATji7wSmzEJoL64DK6PkKat9tvrkfPieMYjxua8ivUfth4oXwGFnDDIR1QBEd4PC-g4rRc4DM1KHRmBzB5bxWEwV6eX6qY3owErcAi0pw/s1600-h/Propagation+Constant+and+Intrinsic+Impedance+of+Lossless+Media.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 225px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgj1-ztZ3sZ5EMgTUAc8NvHz6V4hJYdiG7iIeATji7wSmzEJoL64DK6PkKat9tvrkfPieMYjxua8ivUfth4oXwGFnDDIR1QBEd4PC-g4rRc4DM1KHRmBzB5bxWEwV6eX6qY3owErcAi0pw/s400/Propagation+Constant+and+Intrinsic+Impedance+of+Lossless+Media.JPG" alt="" id="BLOGGER_PHOTO_ID_5427278933819864754" border="0" /></a>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-8454799244714197262010-01-16T16:09:00.000+06:002010-01-16T16:11:45.159+06:00Propagation Constant and Intrinsic Impedance of Good Conducting Media<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWBMw707fY_ZPGmppaTuL5z5dbYOzHErOuwW3416isUzuuOlsBM-W2xw6UH3wph5mcK3-qdizBYTOZyOZSicDBNOQpjO99nSjAh64uRZO-agIFWPn6nk1v0RUwRW6trg41qc0rzA4BRL4/s1600-h/Propagation+Constant+and+Intrinsic+Impedance+of+Good+Conducting+Media.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWBMw707fY_ZPGmppaTuL5z5dbYOzHErOuwW3416isUzuuOlsBM-W2xw6UH3wph5mcK3-qdizBYTOZyOZSicDBNOQpjO99nSjAh64uRZO-agIFWPn6nk1v0RUwRW6trg41qc0rzA4BRL4/s400/Propagation+Constant+and+Intrinsic+Impedance+of+Good+Conducting+Media.JPG" alt="" id="BLOGGER_PHOTO_ID_5427278245460008258" border="0" /></a>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-55051074385886325202010-01-16T16:04:00.000+06:002010-01-16T16:07:35.679+06:00The Group and Phase Velocity Relation<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRqZOyd87Lw_4jYKMs1zz2EvgY4HZShCTLK6V4Uy_iMIMj1CrRg1kdDGAJMefwqTEzQTASjEMSWXEwqNi9SWPMNI5vLPN7pErCxxF27EBfevYCR7qNUqAKj8tQuM2gduCdqK1-ZOw23bo/s1600-h/The+Group+and+Phase+Velocities+of+The+Wave.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 115px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRqZOyd87Lw_4jYKMs1zz2EvgY4HZShCTLK6V4Uy_iMIMj1CrRg1kdDGAJMefwqTEzQTASjEMSWXEwqNi9SWPMNI5vLPN7pErCxxF27EBfevYCR7qNUqAKj8tQuM2gduCdqK1-ZOw23bo/s400/The+Group+and+Phase+Velocities+of+The+Wave.JPG" alt="" id="BLOGGER_PHOTO_ID_5427276983454999234" border="0" /></a>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2813330573840302861.post-56480541988421478742010-01-16T14:57:00.000+06:002010-01-16T15:31:38.190+06:00Pointing Theorem and Explains its Various Terms<meta equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 10"><meta name="Originator" content="Microsoft Word 10"><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:donotshowrevisions/> <w:donotprintrevisions/> <w:donotshowmarkup/> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><style> <!-- /* Font Definitions */ @font-face {font-family:"Angsana New"; panose-1:2 2 6 3 5 4 5 2 3 4; mso-font-alt:"Microsoft Sans Serif"; mso-font-charset:222; mso-generic-font-family:roman; mso-font-format:other; mso-font-pitch:variable; mso-font-signature:16777217 0 0 0 65536 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; mso-bidi-font-size:14.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Angsana New"; mso-bidi-language:TH;} @page Section1 {size:595.3pt 841.9pt; margin:1.0in 10.3pt 1.0in .75in; mso-header-margin:35.4pt; mso-footer-margin:35.4pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> </style><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--><div style="text-align: justify;"><span style="font-size:130%;">The unit of <b style="">E</b> is volt/m and that of <b style="">H</b> is A/m, therefore the product of their magnitudes have the unit of power density. The flow of power due to electromagnetic field in a particular direction is of prime importance, the vector product of <b style="">E</b> and <b style="">H</b> is used to determine the power of an electromagnetic wave.<o:p></o:p></span> </div><p style="text-align: justify;" class="MsoNormal"><span style="font-size:130%;">If we define the power density vector as:<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><b style="">P</b></span><span style="font-size:130%;">=<b style="">E</b></span><span style="font-size:130%;">×<b style="">H</b></span><span style="font-size:130%;"> Watt/m<sup>2</sup>.</span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimK3mUaBwNjpOFl_Q-7xc0NsYW7YS4HKEZ5U7H1nClp9SY4fh5q6p4hjD25095tZyx9Rl8S-t7f6_IOsJgleIBBWJReONdLGJNAqqdVaR3-QOFoCPu_Q-Uv_FqXZBq94Co8hpAUERoWpo/s1600-h/1.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 350px; height: 25px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimK3mUaBwNjpOFl_Q-7xc0NsYW7YS4HKEZ5U7H1nClp9SY4fh5q6p4hjD25095tZyx9Rl8S-t7f6_IOsJgleIBBWJReONdLGJNAqqdVaR3-QOFoCPu_Q-Uv_FqXZBq94Co8hpAUERoWpo/s400/1.JPG" alt="" id="BLOGGER_PHOTO_ID_5427261175539701090" border="0" /></a></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><b style=""><o:p> </o:p></b></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><b style=""><o:p> </o:p></b></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><b style=""><span style=""> </span><o:p></o:p></b></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
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<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">Using the Maxwell’s equations </span><span style="font-size:130%;">we have</span><span style="font-size:130%;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz7vrH5OV57de1qoO88WNk4n6qiCMyLWPS7efJxEEaYGTzV5CQXoKIyW4pg7fU3w_uCZy02FNXzAW4boQyaUHYLiLcmw1EjRDWIHk8tthJHbs4u36u2V629P8tUJWEfXIzfK606FKdR9E/s1600-h/2.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 98px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz7vrH5OV57de1qoO88WNk4n6qiCMyLWPS7efJxEEaYGTzV5CQXoKIyW4pg7fU3w_uCZy02FNXzAW4boQyaUHYLiLcmw1EjRDWIHk8tthJHbs4u36u2V629P8tUJWEfXIzfK606FKdR9E/s400/2.JPG" alt="" id="BLOGGER_PHOTO_ID_5427261179966866434" border="0" /></a></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
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<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">Equation (1) is known as the point form of pointing theorem. Integrating both sides of (1) over some volume v and applying the divergence theorem, we obtain the integral form of </span><span style="font-size:130%;">pointing theorem as follows:</span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUDanhxe-M2SD1ePcUURXeqEKrSF2ozRyvDURMkozQCDvdOEqKjUVMQIUpeBRtqmBBinxcXcOM03ZW4A6CqAaP3NTvtsvC_DX9tEiNqGH1zLBT6EiTFcAQh25IZ_CKF-2d1xeoLjZ0cOQ/s1600-h/3.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 94px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUDanhxe-M2SD1ePcUURXeqEKrSF2ozRyvDURMkozQCDvdOEqKjUVMQIUpeBRtqmBBinxcXcOM03ZW4A6CqAaP3NTvtsvC_DX9tEiNqGH1zLBT6EiTFcAQh25IZ_CKF-2d1xeoLjZ0cOQ/s400/3.JPG" alt="" id="BLOGGER_PHOTO_ID_5427261181674145170" border="0" /></a></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
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<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">The term on the side of (2) is the net inward flux of <b style="">P</b> into the volume v. The First term on the right side of (2) is a power dissipation term in that it represents the rate of expenditure of energy by the electric field. The second term on the right side of (2) is given by</span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWXA6MzpuxSROcacQFkfWy7PxqGtxQng9BNHKeI6IjrI6iMbMbyZZrOvc5Nlf2WOfrZF3Gki83JQHBxwtN0TKL0siStOjaH_3qrtNVGzL4GFcmH9YRcaMabjs3GqHu1NE3cYSPNLCuyNw/s1600-h/4.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 49px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWXA6MzpuxSROcacQFkfWy7PxqGtxQng9BNHKeI6IjrI6iMbMbyZZrOvc5Nlf2WOfrZF3Gki83JQHBxwtN0TKL0siStOjaH_3qrtNVGzL4GFcmH9YRcaMabjs3GqHu1NE3cYSPNLCuyNw/s400/4.JPG" alt="" id="BLOGGER_PHOTO_ID_5427261187927977794" border="0" /></a></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">And represents the time rate of increase of energy stored in the magnetic and electric fields respectively in the volume v.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">
<br /></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-size:130%;">Therefore (2) states that the net inward flux of the pointing vector through some closed surface is the sum of the power dissipated in the volume enclosed by the surface and the rate of change of energy stored in the volume enclosed by the surface.<o:p></o:p></span></p> Unknownnoreply@blogger.com0