The electric field vector e0, the magnetic field vector h0, and. In e and m the energy flux is known as the poynting vector convenient because it points in the direction of the energy flow. Thus this em wave approaches the boundary from the left and is at normal incidence to the boundary. A plane wave is a particular solution to the vector wave equation, where every point on an infinite plane perpendicular to the direction of propagation has the same electric field e v and magnetic field h v in terms of magnitude and direction, see fig. Both the electric field and the magnetic field are perpendicular to the direction of travel x. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when. Simple derivation of electromagnetic waves from maxwells equations. Here, we write down the complex amplitudes for the eb and fields. The simplest electromagnetic waves are uniform plane waves. The dispersion relation can then also be written more compactly as. The conduction current in a conductor is the cause of the di. In many realworld situations, the velocity of a wave depends on its amplitude, so v vf.
We call e 0 the polarization vector for the electric. Electromagnetic waves icecube neutrino observatory. Uniform plane electromagnetic waves in perfect dielectrics. The rate of energy transfer by an electromagnetic wave is described by the poynting vector, s, defined as the rate at which energy passes through a unit surface area perpendicular to the direction of wave propagation wm2. Chapter maxwells equations and electromagnetic waves. We use wave equations instead of transmission line equations 3. If the medium is dispersive different frequencies travel at. Electromagnetic waves maxwells equations predict the propagation.
Lecture 34 electromagnetic scattering cornell university. Here, k is the wave number, which is related to the wavelength of the wave by the equation 2 k. The basic component of energy for an em wave is called a photon. Energy density and the poynting vector overview and. James clerk maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wavelike nature of electric and magnetic fields and their symmetry. Uniform plane waves have uniform constant properties in a plane perpendicular to their direction of propagation. Topic 6 plane wave expansion method pwem topic 7 rigorous coupledwave analysis rcwa. In physics, a plane wave is a special case of wave or field. Derive the frequencydomain wave equation in terms of the electric field for waves in a medium that is linear, homogeneous, and isotropic lhi. The wave is polarized in the x direction by convention, we use the direction of e to specify the polarization of an.
The wave equation is an important secondorder linear partial differential equation for the description of wavesas they occur in classical physicssuch as mechanical waves e. This is a plane wave traveling in the positive zdirection at velocity c. We now use the wave equation to analyze a specific electromagnetic field. Magnetic field of plane wave the magnetic eld of a plane wave in a good conductor can be found using m4. It arises in fields like acoustics, electromagnetics, and fluid dynamics historically, the problem of a vibrating string such as that of a musical. Simple derivation of electromagnetic waves from maxwells. Waves are traveling in dielectric perfect dielectric lossless media 2.
Such polarization states can be generated by superposition of linearly polarized plane waves. As time evolves, the wavefronts propagate at the wave speed without changing. This solution is a wave traveling in the direction of k in the sense that a point of constant phase. The wave equation 3 this is the desired wave equation, and it happens to be dispersionless. Plane electromagnetic waves and wave propagation 7. Electromagnetic plane wave of frequency and wave vector. The wave phase is constant along a planar surface the wavefront.
A wave is disturbance of a continuous medium that propagates with a fixed shape at constant velocity. Superposition of em waves of the same polarization. This function obeys the wave equation, which is a secondorder partial di erential equation. Kshetrimayum 3192014 polarization is the curve traced out by the tip of the arrow representing the instantaneous electric field. This will result in a linearly polarized plane wave travelling in the x direction at the speed of light c.
Derive the frequencydomain wave equation in terms of the magnetic field for waves in a medium that is linear, inhomogeneous, and anisotropic. The uniform plane wave is a fundamental concept in electro magnetics and it is the simplest solution to the maxwells equation for time varying fields in an unbound, homogeneous. For the uniform plane wave described by 19 the plane of uniformity is the xyplane. We will proceed by contour integration in the complex. In this case, the solutions can be hard to determine. Ray kwok example if solar illumination is characterized by a power density of 1 kwm 2 at earths surface, find a the total power radiated by the sun, b the total power intercepted by earth, and. For the dielectric materials used to guide high frequency electromagnetic waves which we will mainly consider here the conductivity is typically zero, while the permeability is that of free space.
In addition to satisfying the wave equation, the complex. The wave equation for a plane electric wave traveling in the x direction in space is. Consider the following three examples of electric fields. The energy e of a photon is proportional to the frequency of radiation f e h f where h is plancks constant 6. Two polarized em waves are incident on the same surface. Radar range equation ece 303 fall 2007 farhan rana cornell university scattering of electromagnetic waves from a plane interface z0 z k ki z. Electromagnetic wave equation hyperphysics concepts.
The symbol c represents the speed of light or other electromagnetic waves. We shall analyze the source terms in the maxwells equations to simplify maxwells equations in. Wave equation from maxwells equations kinda sorta asmr physics. Fortunately, this is not the case for electromagnetic waves. In the absence of free charge and current densities the maxwell equations are. We deal with both normal and nonnormal angles of incidence. E xois complex in general so it has a magnitude je xojand a phase ej since the. In many cases, the electromagnetic wave will not contain all six components. Thus, in addition to a direction k the wave is moving, there is a direction e0 describing which way the electric.
Because the speed of em waves predicted by the wave equation coincided with the measured speed of light, maxwell concluded that light itself is an em wave. Rather than solving the wave equation, we prefer to work directly. Ece 303 fall 2005 farhan rana cornell university waves in a dielectric medium dispersion relation j k r e r n eo e rr rr. Imrana ashraf zahid quaidiazam university, islamabad pakistan. Equations 33 and 34 represent coupled electric and magnetic.
The time average of s over one or more cycles is called the wave intensity, i. What we have here is an example of a plane wave since at any instant bothe andb are uniform over any plane perpendicular to the direction of propagation. For example, a wave on a string is described by the transverse displacement yas a function of xand t. In the presence of absorption, the wave will diminish in size as it move. The wave equation for e and b in vacuum, each cartesian component of e and b satisfies the threedimensional wave equation 2 2 00 2 2 2 2 22 2 00 2 1 t f f vt t. This equation determines the properties of most wave phenomena, not only light waves. Consider a plane wave propagating in the positive z direction. We now want to consider a general plane wave that has arbitrary linear polarization, and travels in any direction.
We refer to intrinsic impedance rather than characteristic impedance, zo 4. The 3d wave equation plane wave spherical wave mit 2. According to quantum physics, the energy of an em wave is quantized, i. In free space, the plane wave propagates with velocity c in direction of the wave vector k kx, ky, kz. Thus the poynting vector represents the ow of energy in the same way that the current jrepresents the ow of charge. In the absence of free charge and current densities the maxwell equations are the wave equations for and are derived by taking the curl of and. This is known as a transverse electromagnetic wave tem, where e, h, and the direction of propagation are perpendicular to each other. The green function of the wave equation for a simpler derivation of the green function see jackson, sec. The wave equation and plane wave solution duration. The electromagnetic wave from maxwells equations contd 2 2 t e e w w u u 2 2 2 t e e e o o w w x ph xe 0 using the vector identity becomes, in free space and. E e b b maxwells equations imply that empty space supports the propagation of electromagnetic waves, traveling at a speed 8 00 1.
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