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An elliptically polarized wave travelling in the +z direction in air has x and y components
Ex = 2 sin(ωt - βz) V/m;
Ey = 4 sin(ωt - βz + 75°) v/m
The average power per unit area conveyed by the wave is
  • a)
    15.8 mW/m2
  • b)
    12mW/m2
  • c)
    26.5 mW/m2
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
An elliptically polarized wave travelling in the +z direction in air h...
The average power per unit area is equal to the Poynting vector, the magnitude of which is given by

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Most Upvoted Answer
An elliptically polarized wave travelling in the +z direction in air h...
Given:
Ex = 2 sin(ωt -βz) V/m;
Ey = 4 sin(ωt -βz + 75°) V/m;

To find:
Average power per unit area conveyed by the wave.

Explanation:

1. Calculate the total electric field:
The total electric field E is given by the vector sum of Ex and Ey:
E = √(Ex² + Ey²)
E = √((2 sin(ωt -βz))² + (4 sin(ωt -βz + 75°))²)
E = √(4 sin²(ωt -βz) + 16 sin²(ωt -βz + 75°))

2. Calculate the average power per unit area:
The average power per unit area is given by:
Pavg = (1/2) * ε₀ * c * E²
Where:
ε₀ = Permittivity of free space = 8.85 x 10^-12 F/m
c = Speed of light = 3 x 10^8 m/s
Substitute the values of ε₀, c, and E into the formula to calculate Pavg.

3. Calculate the angle difference:
The phase difference between Ex and Ey is 75°.
Convert this angle to radians:
75° * (π/180) = 5π/12 radians

4. Substitute and calculate:
Substitute the calculated values of E, ε₀, and c into the formula for Pavg to find the average power per unit area conveyed by the wave.
Therefore, the average power per unit area conveyed by the wave is 26.5 mW/m² (Option C).
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An elliptically polarized wave travelling in the +z direction in air has x and y componentsEx = 2 sin(ωt -βz) V/m;Ey = 4 sin(ωt -βz + 75°) v/mThe average power per unit area conveyed by the wave isa)15.8 mW/m2b)12mW/m2c)26.5 mW/m2d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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