Math Problem Statement

Select the term below is the best one to describe the polarization of a wave with phasor electric field given by Eˉ=2(a^y​−ja^z​)e−jk0​x( V/m)

Solution

The best term to describe the polarization of the wave with the phasor electric field given by:

E=2(a^yja^z)ejk0x(V/m)\vec{E} = 2 (\hat{a}_y - j \hat{a}_z) e^{-jk_0 x} \quad \text{(V/m)}

is circular polarization.

Explanation:

  • The electric field has components in the a^y\hat{a}_y (y-axis) and a^z\hat{a}_z (z-axis) directions.
  • The presence of the imaginary unit jj (or ii) in the a^z\hat{a}_z component indicates that the yy- and zz-components are out of phase by 9090^\circ.
  • When two perpendicular components of the electric field are out of phase by 9090^\circ and have equal magnitudes, the resulting polarization is circular.

Here, a^y\hat{a}_y and a^z\hat{a}_z have equal magnitudes (since 22 is the magnitude for both components), and the phase difference between them is 9090^\circ due to the jj in front of the a^z\hat{a}_z-component. This results in a circular polarization.

Would you like to go deeper into this explanation or ask more about polarization types?


Here are 5 related questions you might find interesting:

  1. How does elliptical polarization differ from circular polarization?
  2. What is the physical meaning of a phasor representation in electromagnetic waves?
  3. How does linear polarization occur from a combination of electric field components?
  4. What role does the propagation constant k0k_0 play in wave behavior?
  5. Can you explain how the Poynting vector relates to the polarization of an electromagnetic wave?

Tip:

Circular polarization can be either left-handed or right-handed, depending on the direction in which the electric field rotates with respect to the direction of wave propagation.

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Math Problem Analysis

Mathematical Concepts

Electromagnetic Waves
Phasor Representation
Polarization of Waves

Formulas

Phasor Electric Field: Eˉ = 2(a^y - ja^z)e−jk0​x

Theorems

Wave Polarization Theorem
Phase Difference in Electromagnetic Waves

Suitable Grade Level

Undergraduate Physics