A plane electromagnetic wave traveling in the positive...

A plane electromagnetic wave traveling in the positive direction of an $x$ axis in vacuum has components $E_{x}=E_{y}=0$ and $E_{z}=(2.0 \mathrm{~V} / \mathrm{m}) \cos \left[\left(\pi \times 10^{15} \mathrm{~s}^{-1}\right)(t-x / c)\right] .(\mathrm{a}) \mathrm{What}$ is the ampli- tude of the magnetic field component? (b) Parallel to which axis does the magnetic field oscillate? (c) When the electric field component is in the positive direction of the $z$ axis at a certain point $P$, what is the direction of the magnetic field component there?

A plane electromagnetic wave traveling in the positive direction of an $x$ axis in vacuum has components $E_{x}=E_{y}=0$ and $E_{z}=(2.0 \mathrm{~V} / \mathrm{m}) \cos \left[\left(\pi \times 10^{15} \mathrm{~s}^{-1}\right)(t-x / c)\right] .(\mathrm{a}) \mathrm{What}$ is the ampli-
tude of the magnetic field component? (b) Parallel to which axis does the magnetic field oscillate? (c) When the electric field component is in the positive direction of the $z$ axis at a certain point $P$, what is the direction of the magnetic field component there?

Key Concepts

Relation Between Electric and Magnetic Fields in Vacuum

In a vacuum, the amplitudes of the electric and magnetic components of an electromagnetic wave are related by the speed of light, typically expressed as E = cB or equivalently B = E/c. This relation provides a direct method to determine one field’s amplitude given the other when the wave propagates in free space.

Transverse Nature of Electromagnetic Waves

The transverse nature of electromagnetic waves means that the oscillations of the electric and magnetic fields occur perpendicular to the direction of wave propagation. This characteristic is a direct consequence of Maxwell's equations and is fundamental to understanding polarized light and wave propagation in media.

Plane Electromagnetic Waves

Plane electromagnetic waves are solutions to Maxwell's equations that describe the propagation of electric and magnetic fields oscillating perpendicular to each other and to the direction of propagation. They illustrate the transverse nature of electromagnetic radiation and the fact that in vacuum both fields travel together at the speed of light.

Right-Hand Rule in Electromagnetism

The right-hand rule is a mnemonic in electromagnetism used to determine the orientation of one vector given the directions of two others, such as in electromagnetic waves where the cross product of the electric and magnetic fields indicates the direction of wave propagation. Understanding this rule is crucial for deducing the correct spatial relationships among the fields.

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