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GATE 2015 EE - SET 2 - Question 9

Solution :

Region 1

y <  0 , \epsilon _{1} =2

Region 2

y > 0 , \epsilon _{2} =5

According to wave propogation ,

  1. The parallel components of the dielectric medium will be the same for both . In this case the components \hat{a_{x}} and \hat{a_{z}} will remain the same for  \vec{E_{1}} and  \vec{E_{2}} .
  2. The perpendicular components of the dielectric medium will be equal (ratio )

\epsilon _{1}\vec{E_{1\perp }} = \epsilon _{2}\vec{E_{2\perp }}  \Rightarrow 2(4\hat{a_{y}})

\Rightarrow 5 E_{2\perp } = E_{2\perp } = \frac{8\hat{a_{y}}}{5} = 1.6\hat{a_{y}}

E_{1} = 3\hat{a_{x}} + 4\hat{a_{y}} + 2\hat{a_{z}}

E_{2} = 3\hat{a_{x}} + 1.6\hat{a_{y}} + 2\hat{a_{z}}

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