GATE EC 2023 Set 1 — Question 20
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Electromagnetics → Plane Waves → Phase & Group Velocity
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Question
Consider a narrow band signal, propagating in a lossless dielectric medium (), with phase velocity and group velocity . Which of the following statement is true? ( is the velocity of light in vacuum.)
Correct answer
(D) vₚ < c, v_g < c
Solution
For a lossless dielectric medium, the phase velocity is given by:Given and .
Substituting these values:Thus, .For a lossless and non-dispersive dielectric medium (where and are constant with frequency), the group velocity is equal to the phase velocity .
Therefore, .
Thus, .Combining these results, both and .
This matches option (D).The final answer is
Substituting these values:Thus, .For a lossless and non-dispersive dielectric medium (where and are constant with frequency), the group velocity is equal to the phase velocity .
Therefore, .
Thus, .Combining these results, both and .
This matches option (D).The final answer is
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