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Introductory Physics Homework Help
Reflection and Transmission of Plane Waves at a Dielectric-Metal Boundary
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[QUOTE="bananabandana, post: 5485351, member: 490819"] [h2]Homework Statement [/h2] Sorry for the dull question. Problem is as shown/attached [ATTACH=full]101341[/ATTACH] [h2]Homework Equations[/h2] The waves in part ii) are traveling in a HIL dielectric of permittivity ##\epsilon_{r}## from ##0 <z<d## and then hit an [I]ideal [/I]metal boundary at ##z=d##. [h2]The Attempt at a Solution[/h2] I figure this should be quite obvious! The total field in the dielectric ##\vec{E_{D}}## is the superposition of the reflected and incident waves. At ##z=d## the field parallel to the boundary must be 0 -ideal metal is ideal conductor and so electrons can move to precisely counteract the field. We also know (from applying Faraday's law to a small loop around the boundary) that the parallel electric field must be continuous across the boundary. i.e $$ \vec{E_{d}} =E_{D}\hat{\mathbf{x}}= \bigg(E_{xi}exp[i(kz-\omega t)] + E_{xr} exp[i(-kz-\omega t) ]\bigg)\hat{\mathbf{x}} $$ [n.b - the frequency of the incident and reflected waves has to be the same, else we couldn't satisfy the boundary condition for all t,] So: $$ E_{D}(z=d) =0 \implies E_{xi} \big[cos(kd) +isin(kd)\big] =-E_{xr} \big[cos(kd)-isin(kd)\big] $$ $$ E_{xr} = -\frac{ cos(kd)+isin(kd)}{cos(kd)-isin(kd)} E_{xi} $$ Which is obviously not the result I'm meant to get! What has gone wrong? [/QUOTE]
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Reflection and Transmission of Plane Waves at a Dielectric-Metal Boundary
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