Arrange the formulas of $\beta$ in the order where plane wave is travelling in lossy dielectric, free space, good conductor, loss-less dielectric respectively. A. $\beta = \omega \sqrt{\frac{\mu \epsilon}{2} [\sqrt{1 + (\frac{\sigma}{\omega \epsilon})^2} +1]}$ B. $\beta = \frac{\omega}{C}$ C. $\beta = \omega \sqrt{\mu \epsilon}$ D. $\beta = \sqrt{\frac{\omega \mu \sigma}{2}}$ Choose the correct answer from the options given below:
Identifying Phase Constant Formulas
The question asks to arrange the formulas for the phase constant ($\beta$) for plane wave propagation in four different media: lossy dielectric, free space, good conductor, and lossless dielectric.
- Formula A: $\beta = \omega \sqrt{\frac{\mu \epsilon}{2} [\sqrt{1 + (\frac{\sigma}{\omega \epsilon})^2} +1]}$ represents the phase constant in a lossy dielectric medium, characterized by the conductivity $\sigma$.
- Formula B: $\beta = \frac{\omega}{C}$ represents the phase constant in free space, where $C$ is the speed of light ($c = 1/\sqrt{\mu_0 \epsilon_0}$).
- Formula C: $\beta = \omega \sqrt{\mu \epsilon}$ is the formula for the phase constant in a lossless dielectric medium.
- Formula D: $\beta = \sqrt{\frac{\omega \mu \sigma}{2}}$ is the approximate formula for the phase constant in a good conductor at high frequencies ($\sigma \gg \omega \epsilon$).
Ordering Beta Formulas by Medium
The required order is: Lossy dielectric, Free space, Good conductor, Lossless dielectric.
Matching the formulas to this order:
- Lossy dielectric: A
- Free space: B
- Good conductor: D
- Lossless dielectric: C
Therefore, the correct sequence is A, B, D, C.
Important Questions from Electromagnetic Wave Propagation
For sky waves, following statements are given:
(A) n > 1, this shows 81 \(\rm\frac{N}{f^2}\) positive
(B) n > 1, show 81 \(\rm\frac{N}{f^2}\) Negative
(C) n < 1 shows 81 \(\rm\frac{N}{f^2}\) < 1
(D) v g x v p= c 2
(E) n = 0 shows 81 \(\rm\frac{N}{f^2}\) = 1, f = f c
Choose the correct answer from the options given below:
If the Polarization vector is given as N and the Direction of propagation is given as K then which one of the following relations is correct?
The wave length (λ) in meters of an electromagnetic wave is related to its frequency (f) in MHz as:
Bending of light wave as it passes between material of different optical density
The wave impedance of a medium is equal to:
