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$$\hat{a_{x}} + 1.6\hat{a_{y}} + 2\hat{a_{z}}$$