GATE EC 2016 Set 2 — Question 34
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Electromagnetics → Maxwell's Equations → Phase & Group Velocity
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Question
Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as , where the propagation constant is a function of the angular frequency . Assume that and are known and are real. From the information available, which one of the following CANNOT be determined?
Correct answer
(D) The power flux through the z = 0 plane.
Solution
Given the electric field:
- (A) Polarization: The electric field vector has only an -component and its phase is constant relative to its direction. Therefore, the wave is linearly polarized in the -direction. This is determined.
- (B) Group velocity (): It is defined as . Since is known, its derivative can be calculated. This is determined.
- (C) Phase velocity (): It is defined as . Since both and are known, is determined.
- (D) Power flux: The time-averaged power flux (Poynting vector) is , where is the intrinsic impedance of the medium. While we know , we do not know the individual values of permeability () and permittivity () for the homogenous medium. Without knowing , the magnitude of the power flux cannot be determined.
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