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A plane electromagnetic wave travels in the z-direction. Its electric field vector is given by: E(z,t) = E0*cos(kz - wt) x-hat + E0*cos(kz - wt + phi) y-hat, where E0 is the electric field amplitude, k is the wave number, w is the angular frequency, and phi is the phase difference between the x and y components. Which of the following statements are correct?

1. If phi = pi/2, the wave is circularly polarized.
2. If phi = pi, the wave is linearly polarized in the xy-plane.
3. The magnetic field vector of the wave is perpendicular to both the electric field vector and the direction of propagation.
4. For phi = pi/2, doubling the amplitude of the y-component of the electric field produces elliptical polarization.

Correct answer: The magnetic field vector of the wave is perpendicular to both the electric field vector and the direction of propagation.

Solution

With phi=pi/2 and equal amplitudes E0, the tip of E traces a circle, confirming circular polarization (A correct). With phi=pi, E = E0*cos(kz-wt)*(x-hat - y-hat), a linearly polarized wave along (x-y) direction (B correct). Option C is always true for any EM wave: B is perpendicular to E and to the propagation direction (C correct). For phi=pi/2 with y-amplitude doubled to 2E0, Ex=E0*cos and Ey=2E0*sin, giving an ellipse (D correct). All four options are correct; this is a multiple-correct type question.

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