An electromagnetic wave in vacuum has the electric and...

An electromagnetic wave in vacuum has the electric and magnetic fields $\vec{E}$ and $\vec{B}$, which are always perpendicular to each other. The direction of polarizations is given by $\vec{X}$ and that of wave propagation by $\vec{k}$ Then $[2012]$ (A) $\vec{X} \| \vec{E}$ and $\vec{k} \| \vec{E} \times \vec{B}$ (B) $\vec{X} \| \vec{B}$ and $\vec{K} \| \vec{E} \times \vec{B}$ (C) $\vec{X} \| \vec{E}$ and $\vec{k} \| \vec{B} \times \vec{E}$ (D) $\vec{X} \| \vec{B}$ and $\vec{k} \| \vec{B} \times \vec{E}$

An electromagnetic wave in vacuum has the electric and magnetic fields $\vec{E}$ and $\vec{B}$, which are always perpendicular to each other. The direction of polarizations is given by $\vec{X}$ and that of wave propagation by $\vec{k}$ Then $[2012]$
(A) $\vec{X} \| \vec{E}$ and $\vec{k} \| \vec{E} \times \vec{B}$
(B) $\vec{X} \| \vec{B}$ and $\vec{K} \| \vec{E} \times \vec{B}$
(C) $\vec{X} \| \vec{E}$ and $\vec{k} \| \vec{B} \times \vec{E}$
(D) $\vec{X} \| \vec{B}$ and $\vec{k} \| \vec{B} \times \vec{E}$

Key Concepts

Electromagnetic Waves

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space. In vacuum, these fields are mutually perpendicular and in phase, and they transport energy and momentum without requiring a medium for propagation.

Polarization

Polarization refers to the orientation of the electric field vector in an electromagnetic wave. In many cases, particularly with plane waves in free space, the polarization is taken to be in the direction of the electric field, meaning that the wave's oscillations occur along that vector.

Wave Propagation Direction

The direction in which an electromagnetic wave travels is given by the propagation vector, often identified with the Poynting vector. The Poynting vector is defined as the cross product of the electric and magnetic fields, indicating the direction in which energy is transmitted.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the vector resulting from a cross product. In the context of electromagnetic waves, if you point the fingers of your right hand in the direction of the electric field and curl them toward the magnetic field, your thumb points in the direction of wave propagation.

Vector Cross Product

The vector cross product is an operation on two vectors that produces a third vector perpendicular to both. This mathematical tool is crucial in electrodynamics for establishing the relationship between the electric field, magnetic field, and the direction of wave propagation.

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