What about the magnetic field? 3 0 obj 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. 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 In this case an envelope of a standing wave will be demonstrated. 1 0 obj 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. 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 … conductor (σ 2 >> ωε 2), show that θ t is complex and tends to zero regardless of the angle of incidence. ��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��� 4 0 obj 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. conductor interface in a similar way to that used for a nonconductor-nonconductor interface. 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 �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� Derive the expression for the propagation factor in medium 2 when e 2(sin cos )xz tt σ 2 >> ωε 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. But the boundary conditions on E have that . \���7�5:��d �۫P���?K �Y���rnb�?������%^�L�S����C>�IU���B帛K��`�Ua��=:��@� v0/�o3>qLQb+7з5����6)��(�k����C"Jr^j���\$�w�ݞ+%���(I�'�EbŚ��N� ��j�a�q�^�:��WS&�}x��&6b�+OMN��1Ղ�' Let’s check and . First, note that this may seem at first glance to be a violation of the “lossless” assumption made at the beginning of this section. 1 2E? <> We’ll look only at the case of normal incidence here. 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. Recall that , since and . 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! �;��(#&9�}Ii�9 ���[��s�PR�{tr���RiX�L��ӓ6z�t�f���80᳔z�m��x &�-�d]�̑~��3_�A�Fp~R1�!xɽ. stream 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. The total field is: . Let’s check and . endobj Now there is: �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! 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 <>/Metadata 1069 0 R/ViewerPreferences 1070 0 R>> 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. endobj ;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�. 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! As before, we start with the boundary conditions in linear media derived 1E? !� <> ����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��� While it is true that we <>/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>> %PDF-1.7 Normal incidence TE Oblique Perfect incidence conductor 2 Electromagnetic Field Theory by R. S. Kshetrimayum 3/20/2018 Lossless medium Good conductor Fig. A second case of practical interest is when Region 2 is a perfect conductor. Recall that , … x��]�o�8�^���>ڇ�">DR���cw{����^qػj�6�s��4���fH�N"N�Ȥ,� ٌ�����d1e� � endobj Plane Waves Part – II 1. %���� 6.1 Plane waves reflection from media interface medium TM 1.2.2 Normal incidence of a plane wave on a perfect conductor surface. 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.