Simple derivation of electromagnetic waves from maxwells. Electrostaticscoulombs law and electric field intensity fields due to continuous charge distributions, electric flux density, gauss law and its applications, electric potential, relations between e and v, maxwells two equations for electrostatic fields, energy density, illustrative problems. Find materials for this course in the pages linked along the left. Chapter 5 the acoustic wave equation and simple solutions. Plane waves a uniform plane wave is a particular solution of maxwells equations with e assuming the same direction, same magnitude, and same phase in infinite planes perpendicular to the direction of propagation similarly for h.
In the absence of free charge and current densities the maxwell equations are. In certain special cases, however, it is more convenient to describe the wave field in a different mathematical form. Wave propagation in perfect dielectric medium uniform. The electric and magnetic fields are orthogonal to the direction of propagation. Wave propagation in perfect dielectric medium uniform plane. Wave is unconstrained in plane orthogonal to wave direction, i. In free space the phase velocity is equal to the speed of light,c. Uniform plane wave article about uniform plane wave by the. Uniform plane waves have uniform constant properties in a plane perpendicular to their direction of propagation. In particular, we examine questions about existence and. Jan 10, 2008 lecture series on transmission lines and e. This latter solution represents a wave travelling in the z direction. Consider the following three examples of electric fields.
Uniform plane wave solution to maxwells equations brian k. Lail 1 introduction solutions to maxwells equations produce the electromagnetic. In terms of energy, the wave phenomenon is defined as the exchange of two different forms of energy. Chapter 3 uniform plane waves university of houston. A uniform plane wave in air is normally incident on an infinitely thick slab. In this section, we solve these equations for the special case of a uniform plane wave. Created by the best teachers and used by over 51,00,000 students. Plasma astrophysics february 17, 2016 these slides are largely based o of 4. Lecture 7 more on constitute relations, uniform plane wave. This function obeys the wave equation, which is a secondorder partial di erential equation. Wave propagation in perfect dielectric medium video lecture from uniform plane wave chapter of electromagnetic theory subject for engineering students. Physics videos by eugene khutoryansky 271,272 views. Feb 29, 2020 a uniform plane wave is one for which both e. Turning to the downlink radiations, throughout this study we assume that the electric field emitted by the base station is considered as a uniform plane wave.
Uniform plane waves in lossless media 39 componentwise, these are. In reality the acoustic wave equation is nonlinear and therefore more complicated than. It arises in fields like acoustics, electromagnetics, and fluid dynamics. Maxwells equations if the boundary conditions are sufficient. Magnetohydrodynamic waves harvardsmithsonian center. Uniform plane waves do not exist in practice because they cannot be produced by. Module 02 uniform plane wave equation and power balance awab sir.
C, a obtain the phasor expressions for the transmitted field e t, h t, and b verify that the average power transmitted into medium 2 vanishes. Chapter 5 the acoustic wave equation and simple solutions 5. Pdf polarization of the uniform plane wave shreyans. In the physics of wave propagation, a plane wave also spelt plane wave is a wave whose wavefronts surfaces of constant phase are infinite parallel planes. Uniform plane waves propagation in free space starting with point form of maxwells equations for time varying fields in free space. Electric and magnetic field are perpendicular to each other no electric or magnetic field in the direction of propagation transverse electromagnetic wave. To obtain the wave equations, differentiate the first w. The uniform plane wave is defined as the magnitude of the electric and magnetic fields. No electric of magnetic field in direction of propagation 3. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when a the angle of incidence is equal to the brewster angle with e field perpendicular to the plane of incidence. The wave equations for free space in a perfect dielectric containing no charges.
In linear uniform media, a wave solution can be expressed as a superposition of plane waves. University of calgary seismic imaging summer school august 711, 2006, calgary abstract abstract. Also, remember that the orientation of the e field of a uniform plane electromagnetic wave is perpendicular to the h field of that wave and that both are perpendicular to the direction from which the wave propagates so far we have come across some useful expressions such as. They are the same at all points in the direction of propagation. Ranga rodrigo university of moratuwa uniform plane waves november 7, 2008 11 51. Plane electromagnetic waves and wave propagation 7. Chapter 2 uniform plane wave equation and power balance. So generally, e x z,t f xvty vtz vt in practice, we solve for either e or h and then obtain the. The wave is polarized in the x direction by convention, we use the direction of e to specify the polarization of an. Rather than solving the wave equation, we prefer to work directly.
This conclusion is a direct consequence of the fact that maxwells equations require the electric field to be proportional to the curl of the magnetic field and viceversa. Here is an illustration of the wavefronts of a plane wave traveling in 3space free image from wikipedia. One of the simplest examples of a boundary value problem is that of a uniform plane. If a wave is uniform over a plane, then the electric and magnetic field vectors must lie in this plane. 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. For electromagnetism in an isotropic medium with index of refraction n, the phase velocity is cn, which equals the group velocity if the index is not frequencydependent. This will result in a linearly polarized plane wave travelling. The mathematics of pdes and the wave equation michael p. We will use these to derive the wave equation for em waves. The simplest electromagnetic waves are uniform plane waves. In uniform plane wave theory we will arrive at a situation that considering tem wave travelling in z direction with electric field having only x component and magnetic field having only y component. Here is an illustration of the wavefronts of a plane wave travelling in 3space the elec. Electric and magnetic field components in propagation direction are zero.
Uniform plane waves 1 free download as powerpoint presentation. In practice, plane wave does not exist because practical wave sources are always finite in extent. Despite being a special case, the solution turns out to be broadly applicable, 9. The time varying fields which can exist in an unbound, homogeneous medium, are constant in a plane containing the field vectors and have wave motion. Plane waves are the basic tools of fourier analysis, which represents the wave field as a sum of purely harmonic waves, and so, resting on the unidirectional feature of such waves, determines the directional content of the wave field. Magnetohydrodynamic waves nick murphy harvardsmithsonian center for astrophysics astronomy 253.
A uniform plane wave with perpendicular polarization represented by eqs. Shevgaonkar, dept of electrical engineering, iit bombay for more details on nptel visit. Lecture8 wave equations and plane wave solution duration. Here, we will look into depth more into various kinds of constitutive relations.
The wave travels a distance equal to one wavelength in one time period. Hence, e and h for each travelling wave are related through a simple multiplication operation. The main reason one would choose to work with the complex exponential form of the plane wave is because complex exponentials are often algebraically easier to work with than the trigonometric sines and cosines. A plane wave in free space propagates with phase velocity equal to the speed of light. The sign the product depends on the direction of power. Uniform plane waves derivation engineering libretexts. Here, k is the wave number, which is related to the wavelength of the wave by the equation 2 k. For the uniform plane wave described by 19 the plane of uniformity is the xyplane. Uniform plane wave in free space we have previously established the following properties of plane waves in free space. Differential form of maxwells equation stokes and gauss law to derive integral form of maxwells equation some clarifications on all four equations timevarying fields wave equation example. In reality the acoustic wave equation is nonlinear and therefore more complicated than what we will look at in this chapter. A uniform plane wave with perpendicular polarization. Plane wave phase and group velocity wave impedance 2. Chapter maxwells equations and electromagnetic waves.
Hirschberg eindhoven university of technology 28 nov 2019 this is an extended and revised edition of iwde 9206. Uniform plane waves in time domain in free space these waves are known as uniform plane waves. For example, a wave on a string is described by the transverse displacement yas a function of xand t. Convection and conduction currents, dielectric constant, lsotropic and homogeneous dielectrics. The velocity of the peak of the wave position of constant phase requires that so the velocity of propagation is. The wave equation reduces to a simple form where e and h are considered to be independent of two dimensions x and y for uniform plane propagating in the z direction, e may have. We have seen that there are solutions of the wave equation which correspond to plane waves, and that any electromagnetic wave can be described as a superposition of many plane waves. In addition, the wave is transverse because both fields are perpendicular to the direction of propagation. In the physics of wave propagation, a plane wave also spelled planewave is a wave whose wavefronts surfaces of constant phase are infinite parallel planes. Consequently, the solution found in this way satisfies all the necessary equations and is a legitimate solution of maxwells. Electromagnetic wave equation in free space uniform plane wave solutions of the wave equation energy and power of electromagnetic waves ece 303 fall 2007 farhan rana cornell university basic wave motion v.
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