GATE EC 2014 Electromagnetics Solution Q 3

GATE EC 2014 Electromagnetics Solution Q 3

Assume that a plane wave in air with an electric field \overrightarrow E=10\cos\left(\omega t-3x-\sqrt3z\right){\overset\frown a}_yV/m is incident on a non-magnetic dielectric slab of relative permittivity 3 which covers the region z>0 . The angle of transmission in the dielectric slab is ______degrees.

Ans :300

Explanation

\varepsilon_{r1}=1\;and\;\varepsilon_{r2}=3 {}^1\mu_2=\frac{\mu_2}{\mu_1}=\frac{\sin\;\theta_1}{\sin\;\theta_2} \mu_1\sin\;\theta_1=\mu_2\sin\;\theta_2

\sin\theta_1=\sqrt3.\sin\theta_2…..(1)

Now from the given equation of E, we can calculate the angle of incidence

GATE EC 2014 Electromagnetics Solution img2 - Grad Plus
\tan\;\theta_1=\frac3{\sqrt3}=\sqrt3\;\;\;\;\;\;\Rightarrow\;\;\;\theta_1=60^o

Put this value of \begin{array}{l}\theta_1\\\end{array} in eq. 1 we get

\begin{array}{l}\sin60^0=\sqrt3.\sin\theta_2\\\end{array} \begin{array}{l}\therefore\theta_2=30^0\\\end{array}

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