The magnetic component of a polarized wave of light is given...

The magnetic component of a polarized wave of light is given by $B_{x}=(4.00 \mu \mathrm{T}) \sin \left[k y+\left(2.00 \times 10^{15} \mathrm{~s}^{-1}\right) t\right] .$ (a) In which direction does the wave travel, (b) parallel to which axis is it polarized, and (c) what is its intensity? (d) Write an expression for the electric field of the wave, including a value for the angular wave number. (e) What is the wavelength? (f) In which region of the electromagnetic spectrum is this electromagnetic wave?

The magnetic component of a polarized wave of light is given by $B_{x}=(4.00 \mu \mathrm{T}) \sin \left[k y+\left(2.00 \times 10^{15} \mathrm{~s}^{-1}\right) t\right] .$ (a) In which direction does the wave travel, (b) parallel to which axis is it polarized, and (c) what is its intensity?
(d) Write an expression for the electric field of the wave, including a value for the angular wave number. (e) What is the wavelength? (f) In which region of the electromagnetic spectrum is this electromagnetic wave?

Key Concepts

Electromagnetic Spectrum Classification

The electromagnetic spectrum classifies electromagnetic waves based on their wavelengths or frequencies. Different regions of the spectrum, such as radio, microwave, infrared, visible, ultraviolet, X-rays, and gamma rays, have distinct physical properties and applications. Identifying the region to which a particular wave belongs helps in understanding its interactions with matter and its possible uses in various technologies.

Angular Frequency and Wave Number

Angular frequency (?) and wave number (k) are parameters that describe the temporal and spatial periodicity of a wave, respectively. They are related by the speed of propagation of the wave in a given medium, as expressed in the relation c = ?/k in vacuum. This relationship is key for converting between time-based and space-based descriptions of wave phenomena.

Electric and Magnetic Field Relationship

In an electromagnetic wave, the electric and magnetic fields are interrelated and perpendicular to each other as well as to the direction of wave propagation. The magnitude of these fields is connected through the speed of light in vacuum. This relationship allows one to deduce one field when the other is known and is a critical component of Maxwell's equations, which govern all electromagnetic phenomena.

Wavelength Determination

The wavelength of an electromagnetic wave is the spatial period of the wave, which is inversely related to its frequency. By using the wave speed (such as the speed of light in vacuum) and the angular frequency or wave number, the wavelength can be calculated. This concept is crucial for understanding the spatial scale of periodic phenomena and for categorizing different types of electromagnetic radiation.

Polarization of Light

Polarization describes the orientation of the oscillations of the electric and magnetic fields in an electromagnetic wave relative to its direction of propagation. In the context of light, specifically polarized light, one of the field components (electric or magnetic) oscillates in a particular direction. Understanding polarization is crucial when analyzing the alignment of the wave’s fields and their interaction with optical elements like polarizers.

Electromagnetic Wave Propagation

Electromagnetic waves are characterized by oscillating electric and magnetic fields that propagate through space. The direction of propagation can be determined by analyzing the phase factor in the wave equation. Specifically, the wave travels in the direction in which the phase argument (the combination of spatial and temporal variables) remains constant. This concept is fundamental to understanding how changes in the spatial coordinate relate to the wave’s movement through the medium.

Intensity of Electromagnetic Waves

The intensity of an electromagnetic wave quantifies the amount of energy it transports per unit area per unit time. It is a property that can be determined from the amplitudes of the electric and magnetic fields. In free space, the intensity is proportional to the square of the field amplitude, and its calculation incorporates constants such as the permittivity of free space and the speed of light. This concept is essential for linking the observable energy distribution in the wave to its underlying field dynamics.

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