Arrange the following media (characterised by their relative dielectric permittivities (εr) and relative magnetic permeabilities (μr)) according to the velocity of an electromagnetic wave propagating in them in ascending order.
(A) εr = 4 and μr = 400
(B) εr = 3 and μr = 300
(C) εr = 4 and μr = 250
(D) εr = 5 and μr = 150
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (C), (B), (D)
The speed of an electromagnetic wave in a medium depends on its permittivity and permeability:
\( \displaystyle v = \frac{1}{\sqrt{\mu\varepsilon}} = \frac{1}{\sqrt{\mu_0\mu_r\,\varepsilon_0\varepsilon_r}} = \frac{c}{\sqrt{\mu_r\varepsilon_r}} \)
So the larger the product \( \varepsilon_r\mu_r \), the slower the wave. Work out the product for each medium:
(A) \( \varepsilon_r = 4,\ \mu_r = 400 \) — \( 4 \times 400 = 1600 \Rightarrow v = c/40 \)
(B) \( \varepsilon_r = 3,\ \mu_r = 300 \) — \( 3 \times 300 = 900 \Rightarrow v = c/30 \)
(C) \( \varepsilon_r = 4,\ \mu_r = 250 \) — \( 4 \times 250 = 1000 \Rightarrow v \approx c/31.6 \)
(D) \( \varepsilon_r = 5,\ \mu_r = 150 \) — \( 5 \times 150 = 750 \Rightarrow v \approx c/27.4 \)
Ascending order of velocity is descending order of the product: (A), (C), (B), (D).