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The electric field of a uniform plane electromagnetic wave in free space, along the positive x direction is given by E = 10(ay+jaz)e-j25x. The frequency and polarization of the wave, respectively, are
- a)1.2GHz and left circular
- b)4 Hz and left circular
- c)1.2GHz and right circular
- d)4 Hz and right circular
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The electric field of a uniform plane electromagnetic wave in free spa...
The field in circular polarization is found to be
propagating in +ve x -direction.
where, plus sign is used for left circular polarization and minus sign for right
circular polarization. So, the given problem has left circular polarization.
where, plus sign is used for left circular polarization and minus sign for right
circular polarization. So, the given problem has left circular polarization.
Most Upvoted Answer
The electric field of a uniform plane electromagnetic wave in free spa...
Frequency and Polarization of a Uniform Plane Electromagnetic Wave
Frequency of the Wave
- The given wave equation is E = 10(ay jaz)e-j25x.
- This wave equation is in the form of a plane electromagnetic wave propagating in the x direction.
- The wave equation contains the term e-j25x, which represents the phase of the wave.
- The frequency of the wave is given by the phase factor of the wave equation, which is 25.
- Therefore, the frequency of the wave is 25/2π = 1.2 GHz.
Polarization of the Wave
- The given wave equation is E = 10(ay jaz)e-j25x.
- The polarization of the wave is determined by the direction of the electric field vector.
- The electric field vector is given by E = 10(ay jaz).
- The electric field vector is perpendicular to the direction of propagation, which is the x direction.
- Therefore, the wave is polarized in the yz plane.
- The electric field vector has components in the y and z directions, which are equal in magnitude.
- The wave is said to have circular polarization if the magnitudes of the y and z components are equal and the phase difference between them is 90 degrees.
- In the given wave equation, the magnitudes of the y and z components are equal and the phase difference between them is 90 degrees.
- Therefore, the wave has left circular polarization.
Final Answer:
The frequency and polarization of the wave are given by 1.2 GHz and left circular, respectively.
Frequency of the Wave
- The given wave equation is E = 10(ay jaz)e-j25x.
- This wave equation is in the form of a plane electromagnetic wave propagating in the x direction.
- The wave equation contains the term e-j25x, which represents the phase of the wave.
- The frequency of the wave is given by the phase factor of the wave equation, which is 25.
- Therefore, the frequency of the wave is 25/2π = 1.2 GHz.
Polarization of the Wave
- The given wave equation is E = 10(ay jaz)e-j25x.
- The polarization of the wave is determined by the direction of the electric field vector.
- The electric field vector is given by E = 10(ay jaz).
- The electric field vector is perpendicular to the direction of propagation, which is the x direction.
- Therefore, the wave is polarized in the yz plane.
- The electric field vector has components in the y and z directions, which are equal in magnitude.
- The wave is said to have circular polarization if the magnitudes of the y and z components are equal and the phase difference between them is 90 degrees.
- In the given wave equation, the magnitudes of the y and z components are equal and the phase difference between them is 90 degrees.
- Therefore, the wave has left circular polarization.
Final Answer:
The frequency and polarization of the wave are given by 1.2 GHz and left circular, respectively.
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