# for normal incidence of the wave on perfect conductor

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conductor interface in a similar way to that used for a nonconductor-nonconductor interface. \���7�5:��d endobj Let’s check and . A second case of practical interest is when Region 2 is a perfect conductor. v0/�o3>qLQb+7з5����6)��(�k����C"Jr^j���\$�w�ݞ+%���(I�'�EbŚ��N� ��j�a�q�^�:��WS&�}x��&6b�+OMN��1Ղ�' endobj Recall that , … If the material in Region 2 is a perfect conductor, then there should be no transmission since the electric field is zero in a perfect conductor. Its name refers to the shape of a wave front (constant phase surfaces, perpendicular to the direction of propagation) of a propagating wave: Fig 1 Plane wave … First, note that this may seem at first glance to be a violation of the “lossless” assumption made at the beginning of this section. �lv^��#���C#+����X��[�x��\��,����崈�=q�c��EDE��d"e�)�@��za�0*���D���e���t;�gh^]�_*P��\$�9��'3\��|�<9&����f��� �O���!�&�,�-[9K�2-�"�ٻ! �۫P���?K �Y���rnb�?������%^�L�S����C>�IU���B帛K��`�Ua��=:��@� But the boundary conditions on E have that . For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when (a) The angle of incidence is equal to the Brewster angle with E field perpendicular to the plane Let’s check and . <> In this case an envelope of a standing wave will be demonstrated. �;��(#&9�}Ii�9 ���[��s�PR�{tr���RiX�L��ӓ6z�t�f���80᳔z�m��x &�-�d]�̑~��3_�A�Fp~R1�!xɽ. 6.1 Plane waves reflection from media interface medium TM Normal incidence TE Oblique Perfect incidence conductor 2 Electromagnetic Field Theory by R. S. Kshetrimayum 3/20/2018 Lossless medium Good conductor Fig. <>/Metadata 1069 0 R/ViewerPreferences 1070 0 R>> 4 0 obj 1 0 obj Normal Incidence Plane Wave Reflection at Perfect Conductor At the boundary, since and are both 0, then:Solution exists for Then, This is our old friend, the standing wave! stream !� ;NvLH�q !��s������WlQ��j����u��uu������)���ڛg�tS_H������0� 9��/\���"�*e��y�d�y��v����n60B� ����ELd0&�"֖�۝K�ߠ{��Ջ\$�_b�v'��a� ƑP�(剝B`�W_n����,�➏`j�� �+���Q�BD� ڤ�x���5"F��=�b�� ����X@`:=R�jqf�����iq{���ݚ֬�fy+o�R��I3�QX��ޠX�t��Wg���r��Whad9Gp����yo�lU-BU��5���Ξ6E������W�. We’ll look only at the case of normal incidence here. �3���~D/Y��}��R���D.s��ɼx��s˥�Hv,�mdmc�x����p��8+\�I��e�@jrV���Yc�%�y�,��D �BZ����'�C�`sQ4�^/��n*��ݧ��V�g(dtM��/6\�� ��#�����m]6� ����9|�4)���ѱs���oH>-�T��E���L�u~5H�t�V ���Ju;g9���q�)���+�N�GβΫ����5Au^_a�m����5z�Ue�i�l�� �9fpCV�a~�L;�"L]e���q|�QV��L�� ���3�O�~�����`���"ГiA�k���stc`@��*�W�4� F ���3*���&V�RE��� Figure 3: Wave Reflection and Transmission at Normal Incidence by a Planar Interface [8] As shown in Figure 3 we assume the wave is travelling perpendicular (normal incidence) to the planar interface formed by the two semi-infinite lossless media as shown in the figure. 3 0 obj <> <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/Annots[ 21 0 R 27 0 R 28 0 R 30 0 R 31 0 R 34 0 R 37 0 R 40 0 R 45 0 R 47 0 R 49 0 R 50 0 R 53 0 R 54 0 R 55 0 R 58 0 R 61 0 R 63 0 R 64 0 R 66 0 R 68 0 R 69 0 R 70 0 R 71 0 R 73 0 R 75 0 R 81 0 R] /MediaBox[ 0 0 595.32 841.92] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Now there is: endobj In the limit of perfect conductivity (i.e., ), the wave does not penetrate into the conductor at all, in which case the internal tangential electric and magnetic fields vanish. Oblique Incidence 7.1 Oblique Incidence and Snel’s Laws With some redeﬁnitions, the formalism of transfer matrices and wave impedances for normal incidence translates almost verbatim to the case of oblique incidence. We saw in Section 7.4 that, at normal incidence, the amplitude of an electromagnetic wave falls off very rapidly with distance inside the surface of a good conductor. Plane Wave – normal incidence www.qwed.eu 2 Plane wave in a free space Theory A plane wave is the simplest form of the Maxwell’s equations solution. 1.2.2 Normal incidence of a plane wave on a perfect conductor surface. 1 2E? Normal Incidence Plane Wave Reflection at Perfect Conductor At the boundary, since and are both 0, then: Solution exists for Then, This is our old friend, the standing wave! ٌ�����d1e� � As before, we start with the boundary conditions in linear media derived 1E? s�|�^1�\L�[q|q�B���D�j��fUB�O�?_���������Ԁ�p���6d����#����8[#>�@�f��A��z�o-� �_�>��o���n!���M�%*?�� ]�P����@�SM�!��y����^�x��N 2 0 obj x��]�o�8�^���>ڇ�">DR���cw{����^qػj�6�s��4���fH�N"N�Ȥ,� While it is true that we What about the magnetic field? ��C��f�y�3���j3�\�m�~8>�lʳ����>m�_��Z��c����䏧O�4�?�h�dI^����,-x���>���d��ɳӧO�bI�*9��� ^�%,�,�F&��N/Ჟ����~9�bߙ���O��>y3/�#=��r�|��I�m*��鿒ӿ>}�h�}���x�p�-l�C�C&��q�i0�R��{2�%W��bpr����OV� �r��� The total field is: . Derive the expression for the propagation factor in medium 2 when e 2(sin cos )xz tt σ 2 >> ωε W����E邢w��E�΁��Z���;03�d��zO;��\$�&��e)9 J/8�h]����6"�_�ЅX"�j,Ü���c������0��s���B*��9~z2U���t���A��W++~5Y���3 %���� %PDF-1.7 Normal incidence means perpendicular to the surface, and let's assume that in your case you are talking about a perfect conductor, a metal, and to make you see easier what would happen, let's make this a mirror. Plane Waves Part – II 1. conductor (σ 2 >> ωε 2), show that θ t is complex and tends to zero regardless of the angle of incidence. In this case, η 2 = 0 since the ratio of electric field intensity to magnetic field intensity is zero in Region 2, and subsequently Γ 12 = − 1 and 1 + Γ 12 = 0. Recall that , since and .