Question

Arrange the following media (characterised by their relative dielectric permittivities \((\varepsilon_r)\) and relative magnetic permeabilities \((\mu_r)\)) according to the velocity of an electromagnetic wave propagating in them in ascending order. (A) \(\varepsilon_r=4,\ \mu_r=400\) (B) \(\varepsilon_r=3,\ \mu_r=300\) (C) \(\varepsilon_r=4,\ \mu_r=250\) (D) \(\varepsilon_r=5,\ \mu_r=150\) Choose the correct answer from the options given below:

• A. (A), (C), (B), (D)
• B. (C), (A), (B), (D)
• C. (B), (A), (C), (D)
• D. (A), (B), (C), (D)

Hint:

For electromagnetic waves in a medium: \[ v=\frac{c}{\sqrt{\mu_r\varepsilon_r}} \] First calculate \(\mu_r\varepsilon_r\) for each medium. Larger \(\mu_r\varepsilon_r\) means smaller wave velocity.

Answer 1

The Correct Option is A

Concept: The speed of an electromagnetic wave in a medium is \[ v=\frac{1}{\sqrt{\mu\varepsilon}} \] or \[ v=\frac{c}{\sqrt{\mu_r\varepsilon_r}} \] Thus, \[ v\propto \frac{1}{\sqrt{\mu_r\varepsilon_r}} \] Hence, larger value of \[ \mu_r\varepsilon_r \] corresponds to smaller velocity.

Step 1:Calculate \(\mu_r\varepsilon_r\) for each medium. For (A), \[ \mu_r\varepsilon_r=400\times4=1600 \] For (B), \[ \mu_r\varepsilon_r=300\times3=900 \] For (C), \[ \mu_r\varepsilon_r=250\times4=1000 \] For (D), \[ \mu_r\varepsilon_r=150\times5=750 \]

Step 2: Arrange in ascending order of velocity. Since \[ v\propto \frac{1}{\sqrt{\mu_r\varepsilon_r}} \] the medium having the largest value of \[ \mu_r\varepsilon_r \] will have the smallest velocity. Therefore, \[ 1600>1000>900>750 \] Hence, \[ v_A<v_C<v_B<v_D \]

Step 3: State the answer. \[ { (A)\;<\;(C)\;<\;(B)\;<\;(D) } \] Hence, the correct option is \[ {(A)} \]