Electromagnetic waves problems and solutions pdf
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- 24: Electromagnetic Waves (Exercises)
- Satellite Meteorology
- Satellite Meteorology
- Electromagnetic wave equation
Classical Electromagnetic Radiation, Second Edition focuses on the classical electrodynamics with emphasis on radiation problems and the wave attributes of the electromagnetic field.
24: Electromagnetic Waves (Exercises)
The direction of the electric field shown in each part of Figure 1 is that produced by the charge distribution in the wire. Is the direction of the magnetic field shown in Figure 2a consistent with the right-hand rule for current RHR-2 in the direction shown in the figure? In which situation shown in the figure will the electromagnetic wave be more successful in inducing a current in the wire?
Electromagnetic waves approaching long straight wires. In which situation shown in the figure will the electromagnetic wave be more successful in inducing a current in the loop? Should the straight wire antenna of a radio be vertical or horizontal to best receive radio waves broadcast by a vertical transmitter antenna? How should a loop antenna be aligned to best receive the signals? Note that the direction of the loop that produces the best reception can be used to determine the location of the source.
It is used for that purpose in tracking tagged animals in nature studies, for example. Under what conditions might wires in a DC circuit emit electromagnetic waves? Give an example of interference of electromagnetic waves. The figure shows the interference pattern of two radio antennas broadcasting the same signal. Explain how this is analogous to the interference pattern for sound produced by two speakers. Could this be used to make a directional antenna system that broadcasts preferentially in certain directions?
An overhead view of two radio broadcast antennas sending the same signal, and the interference pattern they produce. Can an antenna be any length? Explain your answer. If you live in a region that has a particular TV station, you can sometimes pick up some of its audio portion on your FM radio receiver.
Explain how this is possible. Does it imply that TV audio is broadcast as FM? Explain why people who have the lens of their eye removed because of cataracts are able to see low-frequency ultraviolet.
Would this be effective in candlelight? Give an example of resonance in the reception of electromagnetic waves. Illustrate that the size of details of an object that can be detected with electromagnetic waves is related to their wavelength, by comparing details observable with two different types for example, radar and visible light or infrared and X-rays.
Make a list of some everyday objects and decide whether they are transparent or opaque to each of the types of electromagnetic waves. Your friend says that more patterns and colors can be seen on the wings of birds if viewed in ultraviolet light. Would you agree with your friend? The rate at which information can be transmitted on an electromagnetic wave is proportional to the frequency of the wave.
Is this consistent with the fact that laser telephone transmission at visible frequencies carries far more conversations per optical fiber than conventional electronic transmission in a wire? What is the implication for ELF radio communication with submarines? Give an example of energy carried by an electromagnetic wave.
In an MRI scan, a higher magnetic field requires higher frequency radio waves to resonate with the nuclear type whose density and location is being imaged.
What effect does going to a larger magnetic field have on the most efficient antenna to broadcast those radio waves? Does it favor a smaller or larger antenna? Laser vision correction often uses an excimer laser that produces nm electromagnetic radiation. This wavelength is extremely strongly absorbed by the cornea and ablates it in a manner that reshapes the cornea to correct vision defects.
Explain how the strong absorption helps concentrate the energy in a thin layer and thus give greater accuracy in shaping the cornea. Also explain how this strong absorption limits damage to the lens and retina of the eye. Calculate the wavelength of each.
Solution a A radio station utilizes frequencies between commercial AM and FM. What is the frequency of a Solution Find the frequency range of visible light, given that it encompasses wavelengths from to nm. Combing your hair leads to excess electrons on the comb.
How fast would you have to move the comb up and down to produce red light? What is its frequency? What is the distance from the radar station to the reflecting object?
Some radar systems detect the size and shape of objects such as aircraft and geological terrain. Approximately what is the smallest observable detail utilizing MHz radar? Solution 0. If the Sun suddenly turned off, we would not know it until its light stopped coming. Distances in space are often quoted in units of light years, the distance light travels in one year. How far is this in meters? A certain During normal beating, the heart creates a maximum 4. If a new radio station has such an antenna that is Is this in the AM or FM band?
TV-reception antennas for VHF are constructed with cross wires supported at their centers, as shown in Figure 15 The ideal length for the cross wires is one-half the wavelength to be received, with the more expensive antennas having one for each channel. Suppose you measure the lengths of the wires for particular channels and find them to be 1. What are the frequencies for these channels? A television reception antenna has cross wires of various lengths to most efficiently receive different wavelengths.
Conversations with astronauts on lunar walks had an echo that was used to estimate the distance to the Moon. If the round-trip time was 2. The distance to the Moon is calculated from the round-trip time. Radar is used to determine distances to various objects by measuring the round-trip time for an echo from the object.
Assume the emissivity is 0. Assume the helium-neon lasers commonly used in student physics laboratories have power outputs of 0. An AM radio transmitter broadcasts Hint: Half the power will be spread over the area of a hemisphere. Assume that the power spreads uniformly over the area of a sphere with no complications from absorption or reflection.
Note that early radar units leaked more than modern ones do. This caused identifiable health problems, such as cataracts, for people who worked near them. See the figure. Satellite dishes receive TV signals sent from orbit. Although the signals are quite weak, the receiver can detect them by being tuned to resonate at their frequency. Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time -- called pulsed lasers. They are used to ignite nuclear fusion, for example.
Suppose a source of electromagnetic waves radiates uniformly in all directions in empty space where there are no absorption or interference effects. Police radar determines the speed of motor vehicles using the same Doppler-shift technique employed for ultrasound in medical diagnostics. Beats are produced by mixing the double Doppler-shifted echo with the original frequency. Assume the same Doppler-shift formulas are valid with the speed of sound replaced by the speed of light.
On its highest power setting, a microwave oven increases the temperature of 0. Electromagnetic radiation from a 5. What is the maximum electric force it experiences? A turn flat coil of wire A researcher measures the wavelength of a 1.
Consider electromagnetic fields produced by high voltage power lines. The intensity is small enough that it is difficult to imagine mechanisms for biological damage due to it. Discuss how much energy may be radiating from a section of power line several hundred meters long and compare this to the power likely to be carried by the lines. Consider the most recent generation of residential satellite dishes that are a little less than half a meter in diameter.
Construct a problem in which you calculate the power received by the dish and the maximum electric field strength of the microwave signals for a single channel received by the dish.
Among the things to be considered are the power broadcast by the satellite and the area over which the power is spread, as well as the area of the receiving dish.
Conceptual Questions Electromagnetic waves approaching a wire loop. Integrated Concepts: a Calculate the ratio of the highest to lowest frequencies of electromagnetic waves the eye can see, given the wavelength range of visible light is from to nm.
Integrated Concepts Police radar determines the speed of motor vehicles using the same Doppler-shift technique employed for ultrasound in medical diagnostics. Integrated Concepts: On its highest power setting, a microwave oven increases the temperature of 0. Integrated Concepts: Electromagnetic radiation from a 5.
What is the sun's wavelength of maximum emission? What is the Earth's wavelength of maximum emission? After learning about electromagnetic waves and its properties, we will now test you on your knowledge. You were introduced to two very popular equations concerning electromagnetic energy: the speed of light and the energy emitted from photons. The prism then casts a rainbow on the windowsill. You just so happen to have a hand-held radiometer handy; closing your eyes you place the instrument on a specific color of the rainbow. You then open your eyes to see that the radiometer measured the energy from that color at 3.
IE Irodov books questions in General Physics includes the most advanced level of questions that really examine your basics, thinking ability and subject level maturity. In IE Irodov PDF has been presented questions in such a way that students will face no problem what so always in understanding till the core of concepts despite their understanding level. IE Irodov has left no stone unturned to cover all the chapters without any error. It holds good conceptual questions with a variety covering every concept. Explaining IE Irodov Physics problems requires a clear understanding of Physics questions and is very time-consuming. Hence, JEE students are advised to read this solution only in their free time.
Yury G. Smirnov, Dmitry V. Electromagnetic TE wave propagation in an inhomogeneous nonlinear cylindrical waveguide is considered. The permittivity inside the waveguide is described by the Kerr law.
Electromagnetic wave equation
The direction of the electric field shown in each part of Figure 1 is that produced by the charge distribution in the wire. Is the direction of the magnetic field shown in Figure 2a consistent with the right-hand rule for current RHR-2 in the direction shown in the figure? In which situation shown in the figure will the electromagnetic wave be more successful in inducing a current in the wire? Electromagnetic waves approaching long straight wires. In which situation shown in the figure will the electromagnetic wave be more successful in inducing a current in the loop? Should the straight wire antenna of a radio be vertical or horizontal to best receive radio waves broadcast by a vertical transmitter antenna? How should a loop antenna be aligned to best receive the signals?
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B , takes the form:. In most older literature, B is called the magnetic flux density or magnetic induction.
In this article we propose to use special classes of the generalized functions in order to state the correct statement of some diffraction problems of electromagnetic waves by thin conducting screens in the cylindrical waveguides with conducting walls. As the generalized solutions, such mappings are considered which assign a linear functional defined on the linear shell of the set of the functions satisfying the corresponding boundary conditions to every value of longitudinal space coordinate. The traces of the solutions on the cross-section of the cylindrical domain are interpreted in the generalized sense. The infinite sets of linear algebraic equations are derived immediately from the generalized boundary conditions. We show that it is advisable to use the boundary conditions for the normal components of the electromagnetic field. This is a preview of subscription content, access via your institution. Rent this article via DeepDyve.
Abstract: The following sections are included: PLANE ELECTROMAGNETIC WAVES (). REFLECTION AND REFRACTION OF ELECTROMAGNETIC.
Problems & Exercises
Looking for a deeper understanding of electromagnetic wave propagation? Need a resource of practice problems to hone your skills? With selected problems and answers, this study aid is a powerful supplement to the study of wave optics. Covering the basics of wave propagation, reflection, refraction, anisotropic media, interference, diffraction, and coherence, this question-and-answer collection provides the opportunity to solve problems chosen by a mentor with decades of experience instructing students. Whether you're a professor needing representative exam problems, a student learning the field of optics, or an experienced engineer looking for a better grasp of the field, you'll find this supplement of focused problems helpful. Equations and parameters of electromagnetic waves 1.
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