calculus - Help to identify every equation in this meme? - Mathematics Stack Exchange
The first term on the rhs of this equation represents an electric dipole induced because of the relationship of the electric and the magnetic fields in a light beam . There is never a magnetic wave without an electric field and never a magnetic there are a variety of reciprocity relations  that connect the two vector fields. Physical characteristics in relation to biological effects .. VDUs create electric and magnetic fields at frequencies in the kHz range and .. The basic unit of the magnetic flux density can be deduced from Equation to be newton second De même les chirurgiens qui utilisent du matériel électrochirurgical.
This aspect of electromagnetic induction is the operating principle behind many electric generators: Each core stores one bit of data. In integral form, the magnetic field induced around any closed loop is proportional to the electric current plus displacement current proportional to the rate of change of electric flux through the enclosed surface.
The speed calculated for electromagnetic waves, which could be predicted from experiments on charges and currents, [note 2] exactly matches the speed of light ; indeed, light is one form of electromagnetic radiation as are X-raysradio wavesand others.
Maxwell understood the connection between electromagnetic waves and light inthereby unifying the theories of electromagnetism and optics.
Formulation in terms of electric and magnetic fields microscopic or in vacuum version [ edit ] In the electric and magnetic field formulation there are four equations that determine the fields for given charge and current distribution. A separate law of naturethe Lorentz force law, describes how, conversely, the electric and magnetic field act on charged particles and currents.
A version of this law was included in the original equations by Maxwell but, by convention, is included no longer. The vector calculus formalism below, due to Oliver Heaviside  has become standard. It is manifestly rotation invariant, and therefore mathematically much more transparent than Maxwell's original 20 equations in x,y,z components. The relativistic formulations are even more symmetric and manifestly Lorentz invariant. For the same equations expressed using tensor calculus or differential forms, see alternative formulations.
The differential and integral equations formulations are mathematically equivalent and are both useful. Derived limits of exposure are given in Tables 34 and 35 of this publication. The limitations for the whole body average SAR are not sufficiently restrictive, since the distribution of the absorbed energy in the human body can be very inhomogeneous and dependent on the RF exposure conditions. In partial body exposure situations, depending on frequency, the absorbed energy can be concentrated in a limited amount of tissue, even though the whole body average SAR is restricted to less than 0.
The eye may need special consideration. At frequencies below about 1 MHz, exposure limits are selected that will prevent stimulation of nerve and muscle cells. Basic exposure limits refer to current densities induced within body tissues. This is the same order of magnitude as natural body currents. Above Hz, the current density necessary for excitation of nervous tissue increases with frequency, until a frequency is reached at which thermal effects dominate.
Since SAR or induced current density values cannot be measured easily in practical exposure situations, exposure limits in terms of conveniently measurable quantities must be derived from basic limits. Because of the wide frequency range addressed in this publication, a single limit number for occupational exposure is not possible. Recommended derived occupational limits in the frequency range kHz to GHz are provided in Table A conservative approach is recommended for pulsed fields where electric and magnetic field strengths are limited to 32 times the values given in Table 34, as averaged over the pulse width, and the power density is limited to a value of times the corresponding value in Table 34, as averaged over the pulse width.
The possibility that the developing fetus could be particularly susceptible to exposure to RF deserves special consideration. Exposure limits for the general population should be lower than those for occupational exposure. For example, recommended derived limits in the frequency range of kHz GHz are provided in Table 35, which are generally a factor of 5 lower than the occupational limits. Where surveys of RF fields indicate levels of exposure in the workplace in excess of limits recommended for the general population, workplace surveillance should be conducted.
Where surveys of RF fields in the workplace indicate levels of exposure in excess of recommended limits, action should be taken to protect workers. In the first instance, engineering controls should be applied, where possible, to reduce emissions to acceptable levels. Such controls include good safety design and, where necessary, the use of interlocks or similar protection devices.
Administrative controls, such as limitation of access and the use of audible and visible warnings, should be used in conjunction with engineering controls. The use of personal protection protective clothingthough useful under certain circumstances, should be regarded as a last resort to ensure the safety of the worker. Wherever possible, priority should be given to engineering and administrative controls. Where workers could be expected to incur exposures in excess of the limits applicable to the general population, consideration should be given to providing appropriate medical surveillance.
Prevention of health hazards related to RF fields also necessitates the establishment and implementation of rules to ensure: Knowledge in all these areas is inadequate to determine whether such effects exist, and therefore, there is no rational basis for recommendations to protect the general population from possible adverse effects. Future research efforts in the areas of weak-interaction mechanisms on the one hand, and studies of effects on carcinogenesis and reproduction in animals and humans on the other hand, should be coordinated to a high degree.
This coordination can be brought about by focusing funding on research proposals of a multidisciplinary and multi-institutional nature. A high priority should be placed on research that emphasizes causal relationships and dose-effect thresholds and coefficients.
The following is a list of priority areas identified by the Task Group as needing further study. Only a few isolated reports of pulsed field effects are available and it is not possible to identify either the frequency or the peak power domain of importance. Data to assess human health hazard in terms of pulse peak power, repetition frequency, pulse length, and the frequency of the RF in the pulse, are urgently needed in view of the widening application of systems employing high power pulses, mostly radarand involving both occupational and general population exposures.
Similar uncertainties surround possible effects on reproduction, such as increased rates of spontaneous abortion and of congenital malformations. Effects of RF exposure on CNS function, with resulting changes in cognitive function, are also surrounded by uncertainties. In view of the potential importance of these interactions and the disruptive effects of the uncertainty on society, a high priority should be placed on research in this area.
It is important that research efforts be coordinated to clarify rather than increase the level of uncertainty. Research on possible mechanisms, such as weak-field interactions, should be closely coordinated with appropriately designed animal toxicology studies and with human epidemiology.
A substantial amount of experimental evidence implicates responses to amplitude-modulated RF fields, which show frequency and amplitude windows; some responses are dependent on co-exposure to physical and chemical agents. Establishing the significance of effects for human health and their dose-response relationships is of paramount importance. Studies are necessary that identify biophysical mechanisms of interaction and that extend the animal and human studies, in order to identify health risks.
Some, but not all, of the sources of difficulties can be overcome by a suitably designed and implemented case-control study. Such studies are in progress and being planned to study childhood cancer and any effects of ELF fields. It is important that such studies evaluate any exposures to RF radiation.
For this reason, background information has been included in this publication that may appear elementary to some readers, but is essential for those from a different discipline. Much of the confusion and the controversies that exist in the field today arise from individuals of one discipline not fully appreciating the basic facts or theories of another.
In this section, the aim is to summarize briefly the basic physical characteristics of electric, magnetic, and electromagnetic fields in the frequency range Hz GHz. The corresponding wavelengths extend from km to 1 mm. At low frequencies below about 10 MHz and for near-field conditions see section 4the electric E and magnetic H fields must be treated separately.
The quantum energies at these frequencies are extremely small and are not capable of altering the molecular structure or breaking any molecular bonds. The maximum quantum energy at GHz is 1. Although there are other definitions of the radiofrequency RF spectrum, its use in this document covers Hz GHz.
It is convenient to introduce the concept of an electric field to describe this interaction. Thus, a system of electric charges produces an electric field at all points in space and any other charge placed in the field will experience a force because of its presence.
The electric field is denoted by E and is a vector quantity, which means that it has both a magnitude and a direction. The force, F, exerted on a point infinitely small body containing a net positive charge q placed in an electric field E is given by: It is frequently easier and more useful to measure the electric potential, V, rather than the force and charge.
This is because the potential is much less dependent on the physical geometry of a given system e. Electric fields exert forces on charged particles. In an electrically conductive material, such as living tissue, these forces will set charges into motion to cause an electric current to flow.
This current is frequently specified by the current density, J, the magnitude of which is equal to the current flowing through a unit surface perpendicular to its direction. J is directly proportional to E in a wide variety of materials.
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Magnetic fields, like electric fields, are produced by electric charges, but only when these charges are in motion. Magnetic fields exert forces on other charges but, again, only on charges that are in motion. The magnitude of the force F acting on an electric charge q moving with a velocity v in the direction perpendicular to a magnetic field of flux density B is given by: If, instead, the direction of v were parallel to B, then F would be zero.
This illustrates an important characteristic of a magnetic field: The basic unit of the magnetic flux density can be deduced from Equation 2. In the literature, both mks and cgs units are also used to express flux density values. The magnetic field strength H is the force with which the field acts on an element of current situated at a particular point. These equations are very powerful, but for complex systems, such as biological bodies, they are difficult to solve.
One class of their solutions results in wave descriptions of the electric and magnetic fields. When the source charges or currents oscillate and the frequency of oscillation is high enough, the E and H fields produced by these sources will radiate from them. A convenient and commonly used description of this radiation is wave propagation. The basic ideas of wave propagation are illustrated in Fig.
The distance from one ascending, or descending, node to the next is defined as the wavelength, and is usually denoted by lamda. The wavelength and the frequency the number of waves that pass a given point in unit timedenoted by f, are related and determine the characteristics of electromagnetic radiation. Frequency is the more fundamental quantity and for a given frequency, the wavelength depends on the velocity of propagation and, therefore, on the properties of the medium through which the radiation passes.
The wavelength normally quoted is that in a vacuum or in air, the difference being insignificant. However, the wavelength can change significantly when the wave passes through other media. The linking parameter with frequency is the speed of light as expressed in Equation 2. Two idealizations of wave propagation are commonly used: A spherical wave is a good approximation to some electromagnetic waves that occur.
Their wavefronts have spherical surfaces and each crest and trough has a spherical surface. On every spherical surface, the E and H fields are constant. The wavefronts propagate radially outwards from the source and E and H are both tangential to the spherical surfaces. A plane wave is another model that approximately represents some electromagnetic waves. Plane waves have characteristics similar to spherical waves because, at points far from the source, the curvature of the spherical wavefronts is so small that they appear to be almost planar.
The defining characteristics of a plane wave are: For other media and for sinusoidal steady-state fields, the wave impedance includes losses in the medium in which the wave is travelling. In RF plane wave propagation far-fieldthe power crossing a unit area normal to the direction of wave propagation is usually designated by the symbol S. In free space, electromagnetic waves spread uniformly in all directions from a theoretical point isotropic source.
As the distance from the point source increases, the area of the wavefront surface increases as a square of the distance, so that the source power is spread over a larger area. As power density S corresponds also to the quotient of the total radiated power and the spherical surface area enclosing the source, it is inversely proportional to the square of the distance from the source, and can be expressed as: Therefore, in many practical applications only the E field or the H field needs to be measured when the point of measurement is at least one wavelength from the source.
In this case, measurement of E makes possible the determination of H and vice-versa. Comparison of power densities in the more commonly used units for free-space, far-field conditions Note: In the near-field, the E and H fields are not necessarily perpendicular; in fact, they are not always conveniently characterized by waves.
They are often nonpropagating in nature and are sometimes referred to as fringing fields, reactive near-fields, or evanescent modes. Objects located near sources may strongly affect the nature of the fields. For example, placing a probe near a source to measure the fields may change the characteristics of the fields considerably Dumansky et al. When RF fields are incident on a conductive object, RF currents are induced in the object.
These currents produce surface fields that are highly localized to the object and are often referred to as RF hot spots. RF hot spots are better characterized as electric and magnetic fields rather than radiation, since, for many conditions, the fields leading to the hot spot never propagate away from the object. At higher frequencies, the electric and magnetic fields maintain an approximately constant relationship in propagating waves.
In general, the lower the frequency, the less coupled the fields become. This is particularly so when the wavelength is very large with respect to the physical size of the source. In practice, the fields of concern from a hazard perspective will be near-fields at frequencies below about 1 MHz. This proliferation has been accompanied by an increased concern about possible health effects of exposure to these fields Grandolfo et al.
As a result, throughout the world, many organizations, both governmental and nongovernmental, have established safety standards or guidelines for exposure see section Electromagnetic devices already in use and the continuous addition of new sources result in the expansion to new frequencies in the spectrum and the increasing presence of RF fields.
Comprehensive data on existing emission systems, and evaluation of present levels of exposure, are essential for the assessment of potential radiation hazards Repacholi, a; Shandala et al.
In this section, sources of electromagnetic fields, both natural and human-made, in the Hz GHz frequency range are surveyed. The human-made electromagnetic environment consists of fields that are produced either intentionally or as by-products of the use of other devices. Human-made sources in the spectrum considered here, however, produce local field levels many orders of magnitude above the natural background. Therefore, for the practical purposes of hazard assessment, the electromagnetic fields on the earth's surface arise from human-made sources.
According to the treaty of the International Telecommunications Union ITU,the electromagnetic spectrum up to 3 THz is subdivided into 12 frequency bands. These bands are designated by numbers as shown in Table 2; only the bands referred to in this publication are given.
Frequency bands of the electromagnetic spectrum in the frequency range Hz GHz a Band Frequency range Metric Description and symbol number subdivision 3 0. Their strengths and range of frequencies vary widely with geographical location, time of day, and season. Some of these variations are systematic and some are random.
Overall, atmospheric fields have an emission spectrum with the largest amplitude components having frequencies of between 2 and 30 kHz.
Generally, the atmospheric field level decreases with increasing frequency. The geographical dependence is such that the highest levels are observed in equatorial areas and the lowest in polar areas. In the RF range, the black-body radiation follows the Rayleigh-Jeans law and the thermal noise from the earth T about K is 0. The human body also emits electromagnetic fields at frequencies of up to GHz at a power density of approximately 0.
For a total body surface area of about 1. Electromagnetic waves that are able to penetrate this shield are limited to two frequency windows, one optical and the other encompassing radiowaves of frequencies from about 10 MHz to The short-wave boundary of the RF-window is due to energy absorption by molecules contained in the atmosphere primarily O2 and H2Owhereas the long-wave boundary is related to the shielding action of the ionosphere.
RF radiation of cosmic origin observed with earth satellites ranges in magnitude from 1. There are three main types of solar emission.
The first is the so-called background, which is the constant component of the emission observed during periods of low solar activity. The second is the component that displays long-term changes, associated with variations in the number of sunspots. Its main contribution is in the frequency range from MHz to 10 GHz.
The third type of emission arises from isolated radio flares or radio emission bursts. The intensity of such emission can exceed the average intensity of the quiet radiation by a factor of one thousand or more; its duration varies from seconds to hours.
Natural sources of lesser intensity also exist and include the moon, Jupiter, Cassiopeia-A, the universal thermal background radiation at 3 K, hydrogen emissions from ionized clouds, line emissions from neutral hydrogen, the OH radical and, most recently observed, from ammonia. At frequencies of 3 kHz-3 MHz, normal service coverage is provided by ground-wave propagation.
At VLF, propagation over distances of thousands of km is possible using this method. At LF and MF, during night-time, reflections from the ionosphere make propagation up to km possible with little attenuation. At HF, other propagation modes are also possible. At frequencies of 30 MHz GHz, service coverage is provided by line-of-sight short pathsdiffraction intermediate pathsor by forward scattering long paths propagation.
Broadcasting systems vary greatly in terms of their design. This diversity results in somewhat different approaches in evaluating human exposure and potential problems. The situations are significantly different for workers and for the general population.
In the case of some workers, such as those maintaining equipment on broadcasting towers, there is a potential for exposure to strong RF fields.
Workers may also be exposed to strong fields in the close vicinity of towers and particularly broadcasting antennas in the VLF, LF, and MF. In contrast, it is rare for the general population to be exposed to strong RF fields from broadcasting. However, there is simultaneous exposure to more than one source. SAR values ranging from 0. There are also human-made sources of electromagnetic fields used for non-communication purposes, in industry Iscience Sand medicine M.
Because of unavoidable imperfections in the construction, production, and use of ISM equipment, and of fundamental physical laws, there is always unintentional leakage of electromagnetic energy from such equipment.
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As a result, each ISM generator acts as an unintentional source producing signals capable of causing harmful effects, depending upon the amount of leakage. To date, the total number of ISM installations in the world is estimated at million Struzak, With such growth, the number of ISM generators expected by the year will be times greater than it is now.
ISM equipment is usually designed at minimum cost, and, typically, is reduced to the essentials necessary for operation. Frequency stability and spectral purity of the power delivered to the work piece are not normally major objectives. Electromagnetic energy leaks from ISM equipment mainly from the applicator and associated leads e. The amount of energy radiated from the applicator and associated leads depends on the particular arrangement of the devices and the work piece, which together act like an antenna the radiation efficiency of which is usually very low.
However, the radiated power may be considerable if the nominal power is high. The equipment acts as a complex antenna system consisting of coupled radiating surface elements resonating at some unspecified frequencies. Often all the power and control wires are situated close to RF power circuits with no shielding. As a result, a considerable amount of RF energy may be fed into these leads and is conducted outwards at a distance and then reradiated.
Typical applications of equipment generating electromagnetic fields in the range Hz GHz Frequency Wavelength Typical applications 0. The presence of conducting objects can give rise to field strengths higher than those expected from theoretical considerations, since they act as diffracting elements for the electromagnetic fields. Consequently, the presence of such objects in the near-field zone of radio stations makes the area between the radiator and the object potentially more hazardous and indicates that problems of safety should be considered carefully Bernardi et al.
Although measurements as well as theory indicate that there is no high-level exposure from broadcasting stations, the existence of limited areas of relatively high irradiation close to the sources should be checked Dumansky et al. Such situations can exist in proximity to very powerful, ground-level transmitters. In several cases, urban areas are served locally by low-power, in-town repeaters. These are placed, for convenience, on the top of tall buildings; unless properly designed, this creates the possibility of stray fields in a densely populated area directly below the RF source.
A typical, high-power, MF transmitter can have a carrier power of kW, plus up to 50 kW in the sidebands of the propagated field. This is an example of how high field strengths can occur in a space open to the public. Although a broadcasting station's property is usually fenced to keep out unauthorized individuals, the fence may be close to the tower base and people may be able to get as close as a few tens of metres or less from the antenna.
Because the wavelengths involved are so long, a near-field exposure situation may exist and a field strength considerably greater than the theoretical ground-wave field strength is to be expected Bini et al. Local MF transmitters find widespread use in cities, where they provide coverage on "blind spots" or other low-signal receiving areas. Powers range from to W at the amplifier output and much less than that can be expected to be radiated into space.