Electromagnetic wave

As mentioned earlier, the speed of light (usually of light in a vacuum) is used in many areas of physics. Below is an example of an application of the constant c.This knowledge can then be used to simplify the energy density situation a bit. Start with the magnetic energy density and replace it with an expression containing the electric field. Electromagnetic Waves are a set of phenomena broadly categorized as Gamma rays, X-rays, Ultraviolet Rays, Visible light, Infra-red Rays, Microwaves and Radio waves Electromagnetic wave[edit]. Electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum

energy, power, and pressure

Infrared is in the range of the EM spectrum between microwaves and visible light. IR has frequencies from about 30 THz up to about 400 THz and wavelengths of about 100 μm (0.004 inches) to 740 nanometers (nm), or 0.00003 inches. IR light is invisible to human eyes, but we can feel it as heat if the intensity is sufficient.  Anti Electromagnetic Wave Anti radiation protection fabric. Anti-electromagnetic wave radiation power stainless steel round crystal volcanic lava round bio-scalar energy pendant necklace Since power is energy on the move, the notion of power existing in a place doesn't make much sense. Instead we should speak of the power delivered to a place. The boundary between one place and another is described by an area. What's the difference between being inside a room and outside the room? The answer is what side of the doorway you're on. How is this opening described? By its area. The sensible definition of power density is then power per area.EM radiation spans an enormous range of wavelengths and frequencies. This range is known as the electromagnetic spectrum. The EM spectrum is generally divided into seven regions, in order of decreasing wavelength and increasing energy and frequency. The common designations are: radio waves, microwaves, infrared (IR), visible light, ultraviolet (UV), X-rays and gamma rays. Typically, lower-energy radiation, such as radio waves, is expressed as frequency; microwaves, infrared, visible and UV light are usually expressed as wavelength; and higher-energy radiation, such as X-rays and gamma rays, is expressed in terms of energy per photon.  Electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies; this classification is known as the electromagnetic spectrum

Quantitatively, the Doppler effect can be characterized by relating the frequency perceived (f) to the velocity of waves in the medium (c), the velocity of the receiver relative to the medium (vr), the velocity of the source relative to the medium (vs), and the actual emitted frequency (f0): Electromagnetic wave definition is - one of the waves that are propagated by simultaneous Examples of electromagnetic wave in a Sentence. Recent Examples on the Web If possible, keep it.. Unlike mechanical waves, electromagnetic waves don't require the presence of physical medium, and you'll find them hurtling through the emptiness of space without a second thought Radio waves, gamma-rays, visible light, and all the other parts of the electromagnetic spectrum are Electromagnetic radiation can be described in terms of a stream of mass-less particles, called..

Electromagnetic Waves: Electric (red) and magnetic (blue) waves propagate in phase sinusoidally, and perpendicularly to one another. The electromagnetic (EM) spectrum encompasses all wave frequencies, including radio, visible light and X-rays. All EM waves are made up of photons that travel through space until they interact with.. The value of [c] was determined by measuring the electromotive force with which a condenser of known capacity was charged, and then discharging the condenser through a galvanometer, so as to measure the quantity of electricity in it in electromagnetic measure. The only use made of light in the experiment was to see the instruments. The value of [c] found by M. Foucault was obtained by determining the angle through which a revolving mirror is turned, while the light reflected from it went and returned along a measured course. No use whatever was made of electricity or magnetism.

Standing waves. Speed of sound. Doppler effect. Shock wave. Huygens-Fresnel principle. Electromagnetic oscillating circuit. Prism. Subtractive and additive color ..products form a magnetic field that changes the man-made waves emitted by WiFi devices into a And remember that within the RF Radiation part of the electromagnetic spectrum, the higher the.. Definition of electromagnetic wave in the AudioEnglish.org Dictionary. Information about electromagnetic wave in the AudioEnglish.org dictionary, synonyms and antonyms

A leading activist on the issue of electromagnetic radiation and its negative impacts on public health has described the rollout of 5G as a massive health experiment which could become a global.. Magnetic field lines form loops such that all field lines that go into an object leave it at some point. Thus, the total magnetic flux through a surface surrounding a magnetic dipole is always zero. In physics, an electromagnetic wave is a change, periodic in space and time, of an electric field E(r,t) and a magnetic field B(r,t). A stream of electromagnetic waves is referred to as electromagnetic radiation of the wave equation for electromagnetic waves in a dielectric proceeds in exactly the same. way as for the vacuum case above, except with µ0 → µ and 0 → . We therefore end up with a wave velocity..

Electromagnetic wave, also known as EM wave, is the travel path of electromagnetic radiation or EMR. EMR is a form of energy that is emitted and absorbed by charged particles Gauss’s Law basically says that a net amount of charge contained within a region of space will generate an electric field that emanates through the surface that surrounds that region. The different types of electromagnetic radiation shown in the electromagnetic spectrum consists of radio waves, microwaves, infrared waves, visible light, ultraviolet radiation, X-rays, and gamma rays

Electromagnetic Waves - Definition, Equation and Electromagnetic

  1. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves,[6] and transverse sound waves (shear waves) in solids
  2. Electromagnetic Wave Woman and Adolescent Man | Denpa Onna to Seishun Otoko
  3. Given Maxwell's four equations (which are based on observation) we have shown that electromagnetic waves must exist as a consequence. They can have any amplitude E0 (with B0 depending on E0 as will be shown later), any wavelength λ, and be retarded or advanced by any phase φ, but they can only travel through empty space at one wave speed c.

Electromagnetic Waves

Work on the left side first. Substitute the one dimensional wave equation for electricity and find its curl.Radio waves are at the lowest range of the EM spectrum, with frequencies of up to about 30 billion hertz, or 30 gigahertz (GHz), and wavelengths greater than about 10 millimeters (0.4 inches). Radio is used primarily for communications including voice, data and entertainment media.As we learned in an earlier section of this book, waves transfer both energy and momentum without transferring any mass. That might seem obvious for mechanical waves (especially if you've ever been bowled over by a strong ocean wave) but when's the last time you ever felt pressed by a radio wave or knocked down by a beam of light? We just don't experience radiation pressure. Still, it is something we can compute. The electromagnetic waves emitted by this transition is transverse, that is a vector and are mutually perpendicular and perpendicular to the direction of propagation

The radio-frequency range encompasses electromagnetic waves with wavelengths from tens of thousands of kilometers to tenths of a millimeter. The history of radio engineering began with the work.. Mechanical waves and electromagnetic waves are two important ways that energy is transported in the When a balloon is rubbed against a head of hair, astatic electric charge is created causing their.. Well that's interesting. Pressure and energy density are the same thing. The only problem is that with waves there is no single value for the energy density. It's a quantity that fluctuates in time and space. What we really need here are time-averaged values. Such quantities are represented by the symbol between two angle brackets. Like this…

We often want to model an electromagnetic wave (light, microwaves) incident upon periodic structures, such as diffraction gratings, metamaterials, or frequency selective surfaces Broadcast radio waves from KPhET. Wiggle the transmitter electron manually or have it oscillate automatically. Display the field as a curve or vectors

  1. and is given the oddly appropriate name poynting vector, not because someone was making a joke about how vectors "poynt" but in honor of its discoverer, the English physicist John Poynting (1852–1914). Poynting's derivation involves vector mathematics that isn't appropriate for the level of this book. (Translation: I don't understand it.)
  2. Electromagnetic waves are not deflected by electric or magnetic field. These waves can be polarized. Electromagnetic Waves undergo interference and diffraction
  3. The difference in the perceived pitch depending on observer location can be explained by the fact that the siren’s position changes as it emits waves. A wave of sound is emitted by a moving vehicle every millisecond. The vehicle ‘chases’ each wave in one direction. By the time the next wave is emitted, it is closer (relative to an onlooker ahead of the vehicle) to the previous wave than the wave’s frequency would suggest. Relative to an onlooker behind the vehicle, the second wave is further from the first wave than one would expect, which suggests a lower frequency.
  4. Maxwell’s correction shows that self-sustaining electromagnetic waves (light) can travel through empty space even in the absence of moving charges or currents, with the electric field component and magnetic field component each continually changing and each perpetuating the other.
  5. I see a wave speed in there (fλ). We'll use c for this one since it's the first letter in the Latin word for swiftness — celeritas.
  6. Electromagnetic waves are emitted by a variety of electrical and electronic appliances that influence an integral part of our lives. The electromagnetic waves emitted may interfere with other appliances..
  7. Work on the right side second. Substitute the one dimensional wave equation for magnetism and find its time derivative.

The implications are huge. Perhaps there are other forms of electromagnetic waves that are invisible to the human eye. The equations impose no limits on wavelength or frequency. The only requirement is that they propagate with the speed of light in a vacuum.The Doppler effect is a periodic event’s change in frequency for an observer in motion relative to the event’s source. Typically, this periodic event is a wave.Certainly not what I expected, but this is the traditional way to write the power density of an electromagnetic wave. Well… almost. The real equation is written in vector form like this…where E = Energy and m = mass. This is known as the mass-energy equivalence, and it uses the speed of light to interrelate space and time. This not only explains the energy a body of mass contains, but also explains the hindrance mass has on speed.

Maxwell’s Equations

124 - Electromagnetic Waves In this video Paul Andersen details the characteristics of electromagnetic waves. Electromagnetic waves are transverse waves.. Electromagnetic waves comprise combinations of electric and magnetic fields that are mutually compatible in the sense that the changes in one generate the other Electromagnetic (EM) radiation is a form of energy that is all around us and takes many forms, such as radio waves, microwaves, X-rays and gamma rays. Sunlight is also a form of EM energy, but visible light is only a small portion of the EM spectrum, which contains a broad range of electromagnetic wavelengths.EM radiation is created when an atomic particle, such as an electron, is accelerated by an electric field, causing it to move. The movement produces oscillating electric and magnetic fields, which travel at right angles to each other in a bundle of light energy called a photon. Photons travel in harmonic waves at the fastest speed possible in the universe: 186,282 miles per second (299,792,458 meters per second) in a vacuum, also known as the speed of light. The waves have certain characteristics, given as frequency, wavelength or energy.

Types of Electromagnetic Waves and Their Example

The electromagnetic spectrum includes energy ranging from gamma rays to electricity. Laser beam geometries display transverse electromagnetic (TEM) wave patterns across the beam similar to.. The poynting vector is important because it aligns the three vectors of an electromagnetic wave: the electric field, the magnetic field, and the direction of propagation. These three vectors are mutually perpendicular; that is, each is perpendicular to the other two. Their relative arrangement is determined by the right hand rule of the cross product (that is; the × between E and B in the equation).

Electromagnetic Wave Parameters Parameters that describe electromagnetic waves include frequency, wavelength and period. Frequency is cycles per second (Hertz), wavelength is distance.. Radiant photon (Beta photon) does not penertrate into matter . Eletric photon (Gamma photon) peneratrates into matter to create heat transfer in matter and can free electron from matter's substances' atom accoding to Photoelectric effect

Video: What Is Electromagnetic Radiation? Live Scienc

Electromagnetic Waves - The Physics Hypertextboo

Convert wave length, frequency and energy. decimal places. Wave length Well, we actually cancelled out too much stuff. This relationship holds true for all field values, not just the maximum. The ratio of the electric to magnetic fields in an electromagnetic wave in free space is always equal to the speed of light.

In the 1860's and 1870's, a Scottish scientist named James Clerk Maxwell developed a scientific theory to explain electromagnetic waves. He noticed that electrical fields and magnetic fields can couple together to form electromagnetic waves. He summarized this relationship between electricity and magnetism into what are now referred to as "Maxwell's Equations." Although it is true that the electromagnetic wave of energy travels along a conductor at 50 percent to 99 The current in wall outlets is an electromagnetic energy field that is waiting to be transferred via..

Anatomy of an Electromagnetic Wave Science Mission Directorat

This particular example is one dimensional, but there are two dimensional solutions as well — many of them. The interesting ones have electric and magnetic fields that change in time. These changes then propagate away at a finite speed. Such a solution is an electromagnetic wave.Heinrich Hertz, a German physicist, applied Maxwell's theories to the production and reception of radio waves. The unit of frequency of a radio wave -- one cycle per second -- is named the hertz, in honor of Heinrich Hertz.Electromagnetic radiation, is a form of energy emitted by moving charged particles. As it travels through space it behaves like a wave, and has an oscillating electric field component and an oscillating magnetic field. These waves oscillate perpendicularly to and in phase with one another.

Electromagnetic Waves and their Properties Boundless Physic

  1. The electromagnetic spectrum exists as waves of different frequencies and wavelengths. The frequency of a wave represents how many times the wave repeats itself in a certain unit of time
  2. An electromagnetic wave is a stream of light photons. Used in everything from radio to X-rays In many respects, an electromagnetic wave behaves similarly to ripples on water, or to sound traveling..
  3. istration, Science Mission Directorate. (2010). Anatomy of an Electromagnetic Wave. Retrieved [insert date - e.g. August 10, 2016], from NASA Science website: http://science.nasa.gov/ems/02_anatomy
  4. The Doppler effect can be caused by any kind of motion. In the example above, the siren moved relative to a stationary observer. If the observer moves relative to the stationary siren, the observer will notice the Doppler effect on the pitch of the siren. Finally, if the medium through which the waves propagate moves, the Doppler effect will be noticed even for a stationary observer. An example of this phenomenon is wind.
  5. Changing electric fields induce a magnetic field (this is how electromagnets work), and changing magnetic Everyone knows how the electromagnetic wave looks like(see answer by asmesure)
  6. The ratio of speed of light (c) to wavelength (λ) can be substituted in place of f to give the same equation to energy in different terms. Note that energy cannot take any value: it can only exist in increments of frequency times Planck’s constant (or Planck’s constant times c divided by wavelength). Energy of a wave is therefore “quantized. ”

Begin with the definitions of pressure (force per area) and work (force times distance) and see what happens.Ultraviolet light is in the range of the EM spectrum between visible light and X-rays. It has frequencies of about 8 × 1014 to 3 × 1016 Hz and wavelengths of about 380 nm (.000015 inches) to about 10 nm (0.0000004 inches). UV light is a component of sunlight; however, it is invisible to the human eye. It has numerous medical and industrial applications, but it can damage living tissue. Free solutions on mechanics, thermodynamics, electrodynamics, oscillations and waves, optics, atomic and nuclear physics. Based on the textbook I.E. Irodov Problems in General Physics The example shown in the diagram below is consistent with this rule. Check it out for yourself. Mentally pick a pair of vectors coming out of the same point on the wave. Hold your right hand flat in front of your face with your thumb stuck out on the side at a right angle in the shape of an "L". Now rotate your hand until your fingers point in the direction of the electric field and your palm faces in the direction of the magnetic field. If your hand is aligned properly you should be able to fold your fingers so they point in the direction of the magnetic field. (Don't move your thumb.) This action imitates the "crossing" of the electric field into the magnetic field. The direction of this cross product is the poynting vector and is indicated by your thumb. If you've done this activity correctly, your thumb should be point out of the screen toward your face. The orientation of the rest of your hand depends on whether you aligned you fingers with an electric field vector pointing left or right. One of them is easy on the hand and the other makes you look like you're performing some odd form of yoga. Deep, Dark, Progressive House. Новые миксы | New Mixes. Cosmic Waves - Flying Dreams 021 (14.05.2020)

Physics - Waves - The Electromagnetic Spectrum - YouTube

Electromagnetic waves or energy passed through the air from one device to the other. SHIRLEY GRIFFITH: Later, Hertz demonstrated the experiment to his students in a classroom This gives us: pressure = momentum transferred per second per unit area = energy deposited per second per unit area / c = I/c, (where I is the intensity of the beam of light). Waves software mixers and plugin racks seamlessly integrate with any SoundGrid-compatible I/O, streamlining the workflow of studio, live and broadcast engineers worldwide Field lines caused by a magnetic dipole: The field lines created by this magnetic dipole either form loops or extend infinitely. Introduces the different kinds of electromagnetic radiation, from light and microwaves to X-rays and gamma rays

Electromagnetic Wave. Initializing live version. time. waves. 1. This representation of a planeâ€Âpolarized sinusoidal electromagnetic wave shows its perpendicular electric and.. It is the last law in the list — Ampère's law as modified by Maxwell — that is the key. A changing electric field can produce a magnetic field in much the same way as an electric current can produce a magnetic field. Thus, electric charges did not have to flow or even to exist. A changing electric field will generate a changing magnetic field all on its own. This would result in a changing electric field, which would result in a a changing magnetic field, and so on — the whole thing flying away out into empty space at the speed of light.The terms light, electromagnetic waves, and radiation all refer to the same physical phenomenon: electromagnetic energy. This energy can be described by frequency, wavelength, or energy. All three are related mathematically such that if you know one, you can calculate the other two. Radio and microwaves are usually described in terms of frequency (Hertz), infrared and visible light in terms of wavelength (meters), and x-rays and gamma rays in terms of energy (electron volts). This is a scientific convention that allows the convenient use of units that have numbers that are neither too large nor too small.

Alibaba.com offers 134 electromagnetic wave insulation material products. About 19% of these are A wide variety of electromagnetic wave insulation material options are available to you, such as.. Electromagnetic Wave Propagation, Radiation, and Scattering: From Fundamentals to Applications (IEEE Press Series on Electromagnetic Wave Theory) Electromagnetic band gap (EBG) structures have unique properties in controlling the propagation of electromagnetic waves

Electromagnetic wave - Wikiversit

Electromagnetic Waves - YouTub

Radio Frequency Assault On Planet Earth’s Life Support

Once in motion, the electric and magnetic fields created by a charged particle are self-perpetuating—time-dependent changes in one field (electric or magnetic) produce the other. This means that an electric field that oscillates as a function of time will produce a magnetic field, and a magnetic field that changes as a function of time will produce an electric field. Both electric and magnetic fields in an electromagnetic wave will fluctuate in time, one causing the other to change. Electromagnetic waves are produced by the motion of electrically charged particles. These waves are also called electromagnetic radiation because they radiate from the electrically charged particles

Alternative Title: electromagnetic wave Britannic

Visible light is found in the middle of the EM spectrum, between IR and UV. It has frequencies of about 400 THz to 800 THz and wavelengths of about 740 nm (0.00003 inches) to 380 nm (.000015 inches). More generally, visible light is defined as the wavelengths that are visible to most human eyes. Electromagnetic Waves continues the applied approach used in the authors' successful Engineering Electromagnetics. The second book is appropriate for a second course in Electromagnetics that.. Waves and Frequency Ranges. The spectrum of electromagnetic waves has frequencies up to 1024 Hz. This very large range is subdivided into different subranges due to different physical properties

Electromagnetic waves do not need any material for transmission; that is, they can be transmitted in a vacuum. Light is part of this spectrum An electromagnetic wave can thus be defined as a transverse wave with mutually perpendicular electrical and magnetic fields that emanate from it. The electromagnetic spectrum is the complete.. Electromagnetic waves. produced by vibrating electric charges ( when an electric charge move back and forth) and can travel through the space where matter is not present Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic (EM) radiation.Waves were poorly understood until the 1900s, when Max Planck and Albert Einstein developed modern corrections to classical theory.

Electromagnetic waves

Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with other charged particles. Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium to form a resultant wave of greater, lower or the same amplitude Electromagnetic waves are formed when an electric field (shown in red arrows) couples with a magnetic field (shown in blue arrows). Magnetic and electric fields of an electromagnetic wave are..

Gauss’s Law for Magnetism

Electromagnetic Inductions and Electromagnetic Waves Example Problems with Solutions Electromagnetic waves are ubiquitous in nature (i.e., light) and used in modern technology—AM and FM radio, cordless and cellular phones, garage door openers, wireless networks, radar, microwave ovens, etc. These and many more such devices use electromagnetic waves to transmit data and signals.

Electromagnetic Waves

Electromagnetic waves and interference Khan Academ

The Magneto Optical Trap: Experimental setup of Magneto Optical Trap (MOT), which uses radiation pressure to cool atomic species. Atoms are slowed down by absorbing (and emitting) photons.These equations are now decoupled (E and B have their own private equations), which certainly simplifies things, but in the process we've changed them from first to second order (notice all the squares). I know I said earlier that lower order implies easier to work with, but these second order equations aren't as difficult as they look. Raising the order has not made things more complicated, it's made things more interesting. electromagnetic wave definition: The definition of an electromagnetic wave is one that moves by the power of electric and magnetic fields. (noun) An example of an electromagnetic wave is what..

Propagation of an Electromagnetic Wave

Heat transfer through radiation takes place in form of electromagnetic waves mainly in the infrared region. Radiation emitted by a body is a consequence of thermal agitation of its composing molecules There are many variations of laser cooling, but they all use radiation pressure to remove energy from atomic gases (and therefore cool the sample). In laser cooling (sometimes called Doppler cooling), the frequency of light is tuned slightly below an electronic transition in the atom. Because light is detuned to the “red” (i.e., at lower frequency) of the transition, the atoms will absorb more photons if they move towards the light source, due to the Doppler effect. Thus if one applies light from two opposite directions, the atoms will always scatter more photons from the laser beam pointing opposite to their direction of motion (typical setups applies three opposing pairs of laser beams as in ). Know about the inventions, discoveries and other contributions of Michael Faraday including his monumental work in electromagnetism Electromagnetic waves are also known as EM waves that are produced when an electric field It can also be said that electromagnetic waves are the composition of oscillating electric and.. Electromagnetic (EM) waves are changing electric and magnetic fields, transporting energy and For electromagnetic waves E and B are always perpendicular to each other and perpendicular to the..

Electromagnetic Spectrum Wallpapers | HD Wallpapers | ID

Light is made of discrete packets of energy called photons. Photons carry momentum, have no mass, and travel at the speed of light. All light has both particle-like and wave-like properties. How an instrument is designed to sense the light influences which of these properties are observed. An instrument that diffracts light into a spectrum for analysis is an example of observing the wave-like property of light. The particle-like nature of light is observed by detectors used in digital cameras—individual photons liberate electrons that are used for the detection and storage of the image data. Definition: Electromagnetic waves or EM waves are waves that are created as a result of Description: Electromagnetic waves are formed when an electric field comes in contact with a.. Electricity can be static, like the energy that can make your hair stand on end. Magnetism can also be static, as it is in a refrigerator magnet. A changing magnetic field will induce a changing electric field and vice-versa—the two are linked. These changing fields form electromagnetic waves. Electromagnetic waves differ from mechanical waves in that they do not require a medium to propagate. This means that electromagnetic waves can travel not only through air and solid materials, but also through the vacuum of space.Microwaves fall in the range of the EM spectrum between radio and IR. They have frequencies from about 3 GHz up to about 30 trillion hertz, or 30 terahertz (THz), and wavelengths of about 10 mm (0.4 inches) to 100 micrometers (μm), or 0.004 inches. Microwaves are used for high-bandwidth communications, radar and as a heat source for microwave ovens and industrial applications.

[latex]\text{p}=\frac {\text{E}}{\text{c}}=\frac {\text{hf}}{\text{c}}=\frac {\text{h}}{\lambda}[/latex] Transverse Electromagnetic Wave (TEM). This animation shows a linear polarized wave. The relationship between frequency and wavelength is illustrated. (Their product remains constant.. Electromagnetic-acoustic receiving of ultrasound is based on the inverse effect of converting relative to the EMAT-emitting of ultrasound. EMAT-technology of emitting and receiving of ultrasound have some.. IEEE Xplore, delivering full text access to the world's highest quality technical literature in engineering and technology. | IEEE Xplore..

24+ Awesome Wave Logo Designs, Ideas, Examples | DesignBest Electromagnetic Spectrum Illustrations, Royalty-FreeElectromagnetic WavesPhysics Waves Animated Gifs at Best AnimationsSound recorder | 4 things we bet you didn't know EinsteinScalar Weapons - Read It and WeepHeat Clipart Conduction - Hot Weather Clipart Png - FreeAnalysis of the radiation Resistance and Gain of Full-WaveKoala Bears in the Australia Heat Wave of 2009 - YouTube

Light Going from Earth to the Moon: A beam of light is depicted travelling between the Earth and the Moon in the time it takes a light pulse to move between them: 1.255 seconds at their mean orbital (surface-to-surface) distance. The relative sizes and separation of the Earth–Moon system are shown to scale.These equations are first order, which usually means the mathematics should be easy (good!), but they're also coupled, which means it might be difficult (rats!). Let's separate them using this little trick. Take the curl of both sides of Faraday's and Ampère's laws. The left side of each equation is the curl of the curl, for which there is a special identity. The right side of each equation, on the other hand, is the curl of a time derivative. We'll switch it around into a time derivative of the curl.Fast-moving objects exhibit some properties that are counterintuitive from the perspective of classical mechanics. For example, length contracts and time dilates (runs slower) for objects in motion. The effects are typically minute, but are noticeable at sufficiently high speeds. The Lorentz factor (γ) is the factor by which length shortens and time dilates as a function of velocity (v):

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