Uniform plane waves propagation in free space starting with point form of maxwells equations for time varying fields in free space. Tem wave the value of the magnetic field is equal to the magnitude of 7 electromagnetic field theory by r. Similarly to the uplink case, the ambient electric field can be composed of single or multiple plane waves arriving form random directions, with various propagation characteristics. Chapter maxwells equations and electromagnetic waves. Hornbuckle january 27, 2016 1 maxwells equations maxwells equations and the constitutive relations describe the behavior of electromagnetic elds. Wave propagation in perfect dielectric medium uniform plane. A uniform plane wave in air is normally incident on an infinitely thick slab. Uniform plane waves 1 free download as powerpoint presentation. This function obeys the wave equation, which is a secondorder partial di erential equation. Plane wave phase and group velocity wave impedance 2. The wave equations for free space in a perfect dielectric containing no charges. Plasma astrophysics february 17, 2016 these slides are largely based o of 4.
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. In particular, we examine questions about existence and. Uniform plane waves derivation engineering libretexts. Uniform plane wave article about uniform plane wave by the. 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. Uniform plane waves in time domain in free space these waves are known as uniform plane waves. Hence, e and h for each travelling wave are related through a simple multiplication operation. 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. This latter solution represents a wave travelling in the z direction. If a wave is uniform over a plane, then the electric and magnetic field vectors must lie in this plane. The simplest electromagnetic waves are uniform plane waves. Despite being a special case, the solution turns out to be broadly applicable, 9. Ranga rodrigo university of moratuwa uniform plane waves november 7, 2008 11 51.
The wave is polarized in the x direction by convention, we use the direction of e to specify the polarization of an. 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. Shevgaonkar, dept of electrical engineering, iit bombay for more details on nptel visit. Lecture8 wave equations and plane wave solution duration. Rather than solving the wave equation, we prefer to work directly. 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. 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.
No electric of magnetic field in direction of propagation 3. In reality the acoustic wave equation is nonlinear and therefore more complicated than what we will look at in this chapter. Magnetohydrodynamic waves nick murphy harvardsmithsonian center for astrophysics astronomy 253. One of the simplest examples of a boundary value problem is that of a uniform plane. A plane wave in free space propagates with phase velocity equal to the speed of light.
We will use these to derive the wave equation for em waves. Consequently, the solution found in this way satisfies all the necessary equations and is a legitimate solution of maxwells. Wave propagation in perfect dielectric medium video lecture from uniform plane wave chapter of electromagnetic theory subject for engineering students. 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. Here, we will look into depth more into various kinds of constitutive relations. Module 02 uniform plane wave equation and power balance awab sir. To obtain the wave equations, differentiate the first w. In linear uniform media, a wave solution can be expressed as a superposition of plane waves. 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.
Find materials for this course in the pages linked along the left. Chapter 5 the acoustic wave equation and simple solutions 5. Simple derivation of electromagnetic waves from maxwells. Pdf polarization of the uniform plane wave shreyans. For example, a wave on a string is described by the transverse displacement yas a function of xand t. Chapter 2 uniform plane wave equation and power balance. Jan 10, 2008 lecture series on transmission lines and e. 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. Convection and conduction currents, dielectric constant, lsotropic and homogeneous dielectrics. 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. For the uniform plane wave described by 19 the plane of uniformity is the xyplane. Feb 29, 2020 a uniform plane wave is one for which both e.
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. In reality the acoustic wave equation is nonlinear and therefore more complicated than. In the absence of free charge and current densities the maxwell equations are. Consider the following three examples of electric fields. The mathematics of pdes and the wave equation michael p. 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. This will result in a linearly polarized plane wave travelling. The velocity of the peak of the wave position of constant phase requires that so the velocity of propagation is. Physics videos by eugene khutoryansky 271,272 views.
In certain special cases, however, it is more convenient to describe the wave field in a different mathematical form. Uniform plane waves do not exist in practice because they cannot be produced by. In practice, plane wave does not exist because practical wave sources are always finite in extent. Simple derivation of electromagnetic waves from maxwells equations by lynda williams, santa rosa junior college physics department assume that the electric and magnetic fields are constrained to the y and z directions, respectfully, and that they are both functions of only x and t. They are the same at all points in the direction of propagation. Oct 21, 2018 wave propagation in perfect dielectric medium video lecture from uniform plane wave chapter of electromagnetic theory subject for engineering students. Uniform plane wave solution to maxwells equations brian k. 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. 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. 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. So generally, e x z,t f xvty vtz vt in practice, we solve for either e or h and then obtain the. A uniform plane wave with perpendicular polarization.
Lail 1 introduction solutions to maxwells equations produce the electromagnetic. In this section, we solve these equations for the special case of a uniform plane wave. Here, k is the wave number, which is related to the wavelength of the wave by the equation 2 k. A uniform plane wave with perpendicular polarization represented by eqs. Maxwells equations if the boundary conditions are sufficient. Chapter 3 uniform plane waves university of houston. 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. In terms of energy, the wave phenomenon is defined as the exchange of two different forms of energy.
The sign the product depends on the direction of power. Created by the best teachers and used by over 51,00,000 students. Here is an illustration of the wavefronts of a plane wave traveling in 3space free image from wikipedia. The wave travels a distance equal to one wavelength in one time period. The uniform plane wave is defined as the magnitude of the electric and magnetic fields. The electric and magnetic fields are orthogonal to the direction of propagation. Plane electromagnetic waves and wave propagation 7. Lecture 7 more on constitute relations, uniform plane wave.
Uniform plane wave in free space we have previously established the following properties of plane waves in free space. In addition, the wave is transverse because both fields are perpendicular to the direction of propagation. University of calgary seismic imaging summer school august 711, 2006, calgary abstract abstract. 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. Chapter 5 the acoustic wave equation and simple solutions.
118 795 1168 1589 209 630 1379 67 8 1458 844 1117 351 327 1101 384 18 1640 633 1376 1464 906 1110 681 1493 582 360 965 911 1291 599 580 822 1355 1491