The radiation flux density is equal. Electromagnetic radiation flux density – Knowledge Hypermarket
The radiation flux density can vary along certain radiation directions. The amount of energy emitted in the direction /, determined by the angle ty with the normal to the surface n (Fig. 16.1) per unit elementary area per unit time within a unit elementary solid angle 4o, is called the angular radiation density.
The radiation flux density can vary along certain radiation directions. The amount of energy emitted in a certain direction /, determined by the angle r ] with the normal to the surface n (Fig. 16 - 1) unit of an elementary area per unit of time within an elementary solid angle do, is called the angular density of radiation.
The radiation flux density is proportional to the fourth power of frequency.
Radiation flux density E is an integral characteristic relating to the entire wavelength range. Spectral radiation flux density EI dE / dhB characterizes the distribution of radiation energy over wavelengths.
The density of the radiation flux incident on the screen, E (illumination intensity or simply illumination) changes due to the deflection of the rays.
The radiation flux density is determined by the direct and reflected fluxes. The magnitude of the reflected flux depends on the distance between the source and the reflecting surfaces.
Radiation flux density is the amount of radiation energy passing per unit time through a unit surface area within a hemispherical solid angle.
The radiation flux density depends on the angle of incidence of waves on the surface of the body, since with increasing angle of incidence the same radiation flux is distributed over an increasingly larger surface.
The radiation flux density of a gas as a whole is the sum of the radiation flux densities of all bands of its spectrum.
The radiation flux density of a laser beam is characterized by the ratio of the total output power to the area of the heating spot at the focus. An increase in the flux density to 105 - 106 W / cm2 and its distribution over a heating spot with a diameter of 0 25 - 0 5 mm leads to the formation of a narrow channel in the liquid phase, through which radiation penetrates deep into the volume of the material being cut. The presence of this phase in destruction products is a feature of laser processing of metals. It seems quite complex and must be built taking into account thermal and hydrodynamic phenomena.
Efo - radiation flux density corresponding to the angle φ; dQ is the elementary solid angle at which an elementary area on the surface of a hemisphere having a center at this point is visible from a given point of the radiating body; f is the angle between the normal to the radiating surface and the direction of radiation. For real bodies, Lambert's law is satisfied only approximately.
Fnat is the flux density of leakage radiation that reaches the detection point after passing at least part of its initial path through the protection. This consideration does not take into account particles or quanta, the scattering trajectory of which can be conventionally designated as follows: source - filler - protection - filler - detector. This means that the protection material can be considered a completely black body for radiation entering it from the filler.
The concept of radiation flux density is not associated with any idea of the direction of radiation, as a result of which this quantity is intended to characterize equally bright emitters in any direction.
Flux density electromagnetic radiation
/ call the relation electromagnetic energy W passing in time t through a surface of area S perpendicular to the rays, to the product of area S and time t:
In fact it's power electromagnetic radiation(energy per unit time) passing through a unit surface area. Radiation flux density in SI is expressed in watts per square meter(W/m2). This quantity is sometimes called wave intensity.
Let us express I in terms of the density of electromagnetic energy and the speed of its propagation c. Let us choose a surface of area S, perpendicular to the rays, and construct a cylinder with generatrix c t on it as a base (Fig. 7.6). Cylinder volume V=Sc t. Electric energy magnetic field inside the cylinder is equal to the product of energy density and volume: W = c tS. All this energy will pass through the right base of the cylinder in time t. Therefore, from formula (7.1) we obtain
i.e. radiation flux density
is equal to the product of the density of electromagnetic energy and the speed of its propagation.
Let us find the dependence of the radiation flux density on the distance to the source. To do this, we need to introduce another new concept.
Dependence of radiation flux density on the distance to a point source. The energy carried by electromagnetic waves is distributed over a larger and larger surface over time. Therefore, the energy transmitted through the surface of a single area per unit time, i.e., the radiation flux density, decreases with distance from the source.
Let's place a point source at the center of a sphere of radius R. The surface area of the sphere is S = 4 R 2 . If we assume that the source emits the total energy W in all directions during time t, then
The radiation flux density from a point source decreases in inverse proportion to the square of the distance to the source.
Dependence of radiation flux density on frequency. The emission of electromagnetic waves occurs during the accelerated movement of charged particles (see § 48). Tension electric field and magnetic induction of an electromagnetic wave are proportional to the acceleration of the radiating particles. Acceleration at harmonic vibrations proportional to the square of the frequency. Therefore, the electric field strength and magnetic induction are also proportional to the square of the frequency:
The energy density of the electric field is proportional to the square of the field strength. The energy of the magnetic field, as can be shown, is proportional to the square of the magnetic induction. Total Energy Density electromagnetic field equal to the sum of the energy densities of the electric and magnetic fields. Taking into account formula (7.2), the radiation flux density
The radiation flux density is proportional to the fourth power of frequency.
POINTING VECTOR- vector of el-magnetic energy flux density. fields (in the GHS system), where E And N - electrical tension and mag. fields. P.v. modulo equal to the amount of energy transferred through a unit area perpendicular to S , per unit of time. Since components tangential to the interface between two media E And N continuous, vector S continuous at the boundary of two media. Density of quantity of movement of el-magn. fields is determined by the vector S /c 2 . This ratio reveals the materiality of el-magn. fields. P.v. is part of the energy-momentum density tensor electromagnetic field. The concept of P. v. was introduced in Poynting’s theorem 10 years after the general formulation by N.A. Umov (1874) of the concept of energy flow in a medium, therefore P.v. in the literature it is often called the Umov-Poynting vector.
What is common to all waves (regardless of their nature) is that during their propagation, energy is transferred without matter being transferred.
The energy transferred by an electromagnetic wave consists of the energy of electric and magnetic fields.
Bulk Density w The energy of an electromagnetic wave consists of the volume densities of the electric and magnetic fields: 
(4.1)
Taking into account expression (3.5), we find that the energy density of the electric and magnetic fields at each moment of time is the same, i.e. = . That's why (4.2)
Multiplying the energy density w for speed v wave propagation in the medium, we obtain the modulus of energy flux density: (4.3)
Since vectors E And N are mutually perpendicular and form a right-handed system with the direction of wave propagation, then the direction of the vector [EN] coincides with the direction of energy transfer, and the magnitude of this vector is equal to EH.Electromagnetic energy flux density vector called Umov-Poynting vector: S=. (4.4)
Vector S is directed in the direction of propagation of the electromagnetic wave, and its magnitude is equal to the energy transferred by the electromagnetic wave per unit time through a unit area perpendicular to the direction of propagation of the wave.
The intensity is related to the Poynting vector by the relation:
Electromagnetic waves transfer energy from one area of space to another. Energy transfer occurs along rays - imaginary lines indicating the direction of wave propagation. The most important energy characteristic of electromagnetic waves is the radiation flux density. Let's imagine a platform of area S located perpendicular to the rays. Let us assume that during time t the wave transfers energy W through this area. In other words, the radiation flux density is the energy transferred through a unit area (perpendicular to the rays) per unit time; or, which is the same thing, is the radiation power transferred through a single area. The unit of measurement for radiation flux density is W/m2. The radiation flux density is related by a simple relationship with the energy density of the electromagnetic field. We fix the area S, perpendicular to the rays, and a short period of time t. Energy will pass through the area: W = ISt. This energy will be concentrated in a cylinder with base area S and height ct, where c is the speed of the electromagnetic wave. The volume of this cylinder is equal to: V = Sct. Therefore, if w is the energy density of the electromagnetic field, then for the energy W we also obtain: W = wV = wSct. Equating the right-hand sides of the formulas and and reducing by St, we obtain the relation: I = wc. The radiation flux density characterizes, in particular, the degree of influence of electromagnetic radiation on its receivers; When they talk about the intensity of electromagnetic waves, they mean the radiation flux density. An interesting question is how the intensity of radiation depends on its frequency. Let an electromagnetic wave be emitted by a charge performing harmonic oscillations along the X axis according to the law x = x0 sin iet. The cyclic frequency w of charge oscillations will at the same time be the cyclic frequency of the emitted electromagnetic wave. For the speed and acceleration of the charge we have: v = X = x0ш cos Шt and a = v = -x0Ш2 sin Шt. As we see, a ~ w2. The electric field strength and magnetic field induction in an electromagnetic wave are proportional to the acceleration of the charge: E ~ a and B ~ a. Therefore, E ~ w2 and B ~ w2. The electromagnetic field energy density is the sum of the electric field energy density and the magnetic field energy density: w = wel + wMarH. The energy density of the electric field, as we know, is proportional to the square of the field strength: w^ ~ E2. Similarly, it can be shown that wMarH ~ B2. Consequently, w^ ~ w4 and wMarH ~ w4, so w ~ w4. According to the formula, the radiation flux density is proportional to the energy density: I ~ w. Therefore I ~ wA. We have obtained an important result: the intensity of electromagnetic radiation is proportional to the fourth power of its frequency. Another important result is that the radiation intensity decreases with increasing distance to the source. This is understandable: after all, the source radiates in different directions, and as you move away from the source, the emitted energy is distributed over an increasingly larger and larger area. The quantitative dependence of the radiation flux density on the distance to the source is easy to obtain for the so-called point source of radiation. A point source of radiation is a source whose dimensions can be neglected in a given situation. In addition, a point source is assumed to radiate equally in all directions. Of course, a point source is an idealization, but for some problems this idealization works great. For example, when studying the radiation of stars, they can be considered point sources - after all, the distances to the stars are so enormous that their own sizes can be ignored. At a distance r from the source, the emitted energy is uniformly distributed over the surface of a sphere of radius r. The area of the sphere, recall, is S = 4nr2. If the radiation power of our source is P, then during time t energy W = Pt passes through the surface of the sphere. Using the formula, we then obtain: = Pt = P 4 nr2t 4 nr2 Thus, the radiation intensity of a point source is inversely proportional to the distance to it. Types of electromagnetic radiation The spectrum of electromagnetic waves is unusually wide: the wavelength can be measured in thousands of kilometers, or less than a picometer. However, this entire spectrum can be divided into several characteristic wavelength ranges; Within each range, electromagnetic waves have more or less similar properties and methods of radiation.
Ticket
1) The lines indicate the directions of propagation of electromagnetic waves. Lines perpendicular to the surface, at all points of which vibrations occur in the same phases, are called rays. And these surfaces are called wave surfaces.
The flux density of electromagnetic radiation is the ratio of electromagnetic energy ∆W passing through a surface of area S perpendicular to the rays in time ∆t to the product of S by ∆t.
I = ∆W/(S*∆t)
Unit of density magnetic flux in the SI system are watts per square meter (W/m^2). Let us express the flux density through the speed of its propagation and the density of electromagnetic energy.
Let us take a surface S perpendicular to the rays. Let's build a cylinder on it with base c*∆t.
Here c is the speed of propagation of the electromagnetic wave. The volume of the cylinder is calculated by the formula:
∆V = S*c*∆t.
The energy of the electromagnetic field concentrated inside the cylinder will be calculated using the following formula:
∆W = ∆V*ω.
Here ω is the electromagnetic energy density. This energy will pass through the right base of the cylinder in time ∆t. We get the following formula:
I = (ω*c*S*∆t)/(S*∆t) = ω*c.
The energy will decrease as you move away from the source. The following pattern will be true, the dependence of the current density on the distance to the source. The flux density of radiation directed from a point source will decrease in inverse proportion to the square of the distance to the source.
I = ∆W/(S*∆t) = (∆W/(4*pi∆t))*(1/R^2).
Electromagnetic waves are emitted by the accelerated movement of charged particles. In this case, the electric field strength and the magnetic induction vector of the electromagnetic wave will be directly proportional. particle acceleration.
If we consider harmonic vibrations, then the acceleration will be directly proportional to the square of the cyclic frequency. The total energy density of the electromagnetic field will be equal to the sum of the energy density of the electric field and the energy of the magnetic field.
According to the formula I = ω*c, the flux density is proportional to the total energy density of the electromagnetic field.
Dependence of radiation flux density on the distance to a point source. The energy carried by electromagnetic waves is distributed over a larger and larger surface over time. Therefore, the energy transmitted through the surface of a single area per unit time, i.e., the radiation flux density, decreases with distance from the source.
Let's place a point source at the center of a sphere of radius R. The surface area of the sphere is S = 4 R 2 . If we assume that the source emits the total energy W in all directions during time t, then
The radiation flux density from a point source decreases in inverse proportion to the square of the distance to the source.
Dependence of radiation flux density on frequency. The emission of electromagnetic waves occurs during the accelerated movement of charged particles (see § 48). The electric field strength and magnetic induction of an electromagnetic wave are proportional to the acceleration of the radiating particles. Acceleration during harmonic vibrations is proportional to the square of the frequency. Therefore, the electric field strength and magnetic induction are also proportional to the square of the frequency:
2) Diffraction grating - optical instrument, designed to analyze the spectral composition of optical radiation. A diffraction grating consists of thousands of narrow and closely spaced slits. Due to interference, the intensity of light passing through the diffraction grating is different in different directions. There are dedicated areas in which light waves from different slits, the gratings add up in phase, reinforcing each other many times over. When the grating is illuminated with monochromatic light, narrow beams with high intensity are observed at its output. Since the directions to the interference maxima depend on the wavelength, White light, passing through the diffraction grating, will be split into many rays different color. In this way we can study the spectral composition of light. The expression for the interference maxima is the same for a pair of slits and a diffraction grating, but in the latter case the maximum turns out to be much sharper and more intense, providing a high resolution in spectroscopic studies.
EXAMPLE: One of the simplest and most common examples of reflective diffraction gratings in everyday life is a compact disc. On the surface of the CD there is a track in the form of a spiral with a pitch of 1.6 microns between turns. Approximately a third of the width (0.5 µm) of this track is occupied by a recess (this is the recorded data), which scatters the light incident on it, and approximately two-thirds (1.1 µm) is an untouched substrate that reflects the light.
3) Thermonuclear reactions− reactions of fusion (synthesis) of light nuclei occurring at high temperatures. These reactions usually involve the release of energy, since in the heavier nucleus formed as a result of the merger the nucleons are more strongly bound, i.e. have, on average, a higher binding energy than in the original merging nuclei. The excess total binding energy of nucleons is released in the form kinetic energy reaction products. The name “thermonuclear reactions” reflects the fact that these reactions occur at high temperatures ( > 10 7 –10 8 K), since for fusion light nuclei must come close to distances equal to the radius actions nuclear forces attraction, i.e. to distances of ≈10 -13 cm. And outside the zone of action of these forces, positively charged nuclei experience Coulomb repulsion. Only nuclei flying towards each other at high speeds can overcome this repulsion, i.e. included in highly heated environments, or specially accelerated.
The nuclear fusion reaction begins when the colliding nuclei are in the region of their mutual nuclear attraction. In order to get so close, the colliding nuclei must overcome their mutual long-range electrostatic repulsion, i.e. Coulomb barrier.
Coulomb barrier - Atomic nuclei have a positive electric charge. At large distances, their charges can be shielded by electrons. However, in order for the fusion of nuclei to occur, they must approach each other to a distance at which the strong interaction operates. This distance is on the order of the size of the nuclei themselves and many times smaller size atom. At such distances, the electron shells of atoms (even if they were preserved) can no longer shield the charges of the nuclei, so they experience strong electrostatic repulsion. The force of this repulsion, in accordance with Coulomb's law, is inversely proportional to the square of the distance between the charges. At distances on the order of the size of the nuclei, the magnitude of the strong interaction, which tends to bind them, begins to increase rapidly and becomes greater than the magnitude of the Coulomb repulsion.