Which of the following pairs of the component of space and...

Which of the following pairs of the component of space and time varying $\mathrm{E}^{-}=\left(\mathrm{E}_{\mathrm{x}} \mathrm{i} \wedge+\mathrm{Eyj} \wedge+\mathrm{Ezk} \wedge\right)$ and $\mathrm{B}^{-}=\left(\mathrm{B}_{\mathrm{x}} \mathrm{i}^{\mathrm{i}}+\mathrm{Byj}^{\wedge}+\mathrm{Bzk} \wedge\right)$ would generate a plane electromagnetic wave travelling in $+$ ve $z$ direction (A) $E x, B y$ (B) $\mathrm{Ey}, \mathrm{Bz}$ (C) $\mathrm{Ex}, \mathrm{Bz}$ (D) $E z, B x$

Which of the following pairs of the component of space and time varying $\mathrm{E}^{-}=\left(\mathrm{E}_{\mathrm{x}} \mathrm{i} \wedge+\mathrm{Eyj} \wedge+\mathrm{Ezk} \wedge\right)$ and
$\mathrm{B}^{-}=\left(\mathrm{B}_{\mathrm{x}} \mathrm{i}^{\mathrm{i}}+\mathrm{Byj}^{\wedge}+\mathrm{Bzk} \wedge\right)$ would generate a plane
electromagnetic wave travelling in $+$ ve $z$ direction
(A) $E x, B y$
(B) $\mathrm{Ey}, \mathrm{Bz}$
(C) $\mathrm{Ex}, \mathrm{Bz}$
(D) $E z, B x$

Key Concepts

Right-Hand Rule and Direction of Propagation

The direction of wave propagation in an electromagnetic wave is given by the cross product of the electric field and the magnetic field (E × B). Using the right-hand rule, if E is along the x-axis and B is along the y-axis, then the wave propagates in the positive z-direction. This rule ensures that the fields and the direction of travel form a right-handed set.

Polarization

Polarization refers to the orientation of the electric field vector in an electromagnetic wave. Since the magnetic field is always perpendicular to the electric field in a plane wave, the selection of the components (for example, an electric field in the x-direction and a magnetic field in the y-direction) determines the polarization state of the wave.

Plane Electromagnetic Waves

Plane electromagnetic waves are solutions to Maxwell's equations in free space, characterized by constant amplitude and phase fronts that are infinite, parallel planes. In these waves, the electric and magnetic fields oscillate synchronously as they propagate through space.

Transverse Nature of the Fields

In a plane electromagnetic wave, both the electric field (E) and the magnetic field (B) are perpendicular (transverse) to the direction of wave propagation. This means that if the wave is traveling in the z-direction, the field components must lie in the x-y plane.

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