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A 10GHz plane wave travelling in free space has amplitude $E_x=10v/m$. Find 1. The phase constant 2. Intrinsic impedance and 3. The amplitude and direction of

Mumbai University > Electronics Engineering > Sem 5 > Electromagnetic Engineering

Marks: 8 Marks

Year: Dec 2014

1 Answer
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Given:

$f=10 ×10^9 Hz \\ E_x=10 v/m \\ λ=\dfrac{v}{f}=\dfrac{3 ×10^8}{10 ×10^9}=30 ×10^{-3} m \\ β=\dfrac{w}{v}=\dfrac{2πf}{v}=\dfrac{2 × π ×10 ×10^9}{3 ×10^8}=0.21 ×10^3 rad/m$

The intrinsic impedance is given by,

$η=\sqrt{\dfrac{μ}{E}}=\sqrt{\dfrac{μ_o}{E_o}}=120π \\ \text{H (in y direction)}=\dfrac{E_x}{η}=\dfrac{10}{120π}=26.5 mA/m$

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