Topic: Electromagnetics
A plane wave with a frequency of 3 GHz is propagating in an unbounded medium with relative permittivity $\epsilon_{r}=6$ and permeability $\mu_{r}=1.5$, the phase velocity for this wave in this medium is
- A. $1\times 10^{8}\text{ m/s}$
- B. $2\times 10^{8}\text{ m/s}$
- C. $3\times 10^{8}\text{ m/s}$
- D. $1.5\times 10^{8}\text{ m/s}$
Answer: A. $1\times 10^{8}\text{ m/s}$
Explanation: Phase velocity $v_p = \frac{c}{\sqrt{\mu_r \epsilon_r}}$.
Given $\epsilon_r = 6$ and $\mu_r = 1.5$, $\mu_r \epsilon_r = 9$.
$v_p = \frac{3 \times 10^8}{\sqrt{9}} = \frac{3 \times 10^8}{3} = 1 \times 10^8~\text{m/s}$.