The magnetic component of a polarized wave of light is given by Bx=(4.00 μT) sin[k y+(2.00 ×10^1

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

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.

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.

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.

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.

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.

Transcript

00:01 For this problem on the topic of electromagnetic waves, we are given the magnetic component of a polarized way of light to be bx is equal to four macroteslas times a sign of ky plus two times into the power of 15 per second times t.

00:14 We want to first know the direction in which the wave is traveling, the parallel to which axis it is polarized, its intensity.

00:22 You want to write an expression for the electric feel of the wave, including a value for the angular wave number.

00:27 We then want to find its wavelength and the region of the electromagnetic spectrum that this wave is in.

00:34 So firstly, by looking at the term in brackets, we have the sign of ky plus omega -t.

00:42 And so we can see that the plus sign gives us the idea that the wave is traveling in the minus y direction.

00:59 Next for part b, the direction of propagation along the y -axis is perpendicular to b, which is presumably along the x -axis, since the problem gives bx and no other component.

01:10 And both are perpendicular to the electric field e, and thus the wave is z polarized.

01:28 Next, for part c, since the magnetic field amplitude is given as bm is for micro -teslas, which you can read off from the equation, then the electric field field amplitude em is 1 ,100 ,000 ,000 ,000.

01:49 And 99 volts per meter or 1 .2 times 10 to the power 3 volts per meter to these significant figures.

02:02 If we divide this by the square root of 2, we get the rms electric field strength to be 848 volts per meter...

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