tugas quantum

TASK IV: Poynting Vector and Black-body Radiation
Anjar Sari (1017016300991)
Physic Education V

POYNTING VECTOR


Dipole Radiation, Dipole parallel to the z-axis, electric field and poynting-vector in the x-z-plane.
In physics, the Poynting vector can be thought of as representing the energy flux (in W/m2) of an electromagnetic field. It is named after its inventor John Henry Poynting.
Electromagnetic waves carry energy as they travel through empty space. There is an energy density associated with both the electric and magnetic fields. The rate of energy transport per unit area is described by the vector

which is called the Poynting vector. This expression is a vector product, and since the magnetic field is perpendicular to the electric field, the magnitude can be written



which is often called the Abraham form; here E is the electric field and H the auxiliary magnetic field. (All bold letters represent vectors.) Sometimes, an alternative definition in terms of electric field E and the magnetic field B is used, which is explained below. It is even possible to combine the displacement field D with the magnetic field B to get the Minkowski form of the Poynting vector, or use D and H to construct another. The choice has been controversial: Pfeifer et al admirably summarize the century-long dispute between proponents of the Abraham and Minkowski forms.
1. INTERPRETATION
The Poynting vector appears in Poynting's theorem, an energy-conservation law,

where Jf is the current density of free charges and u is the electromagnetic energy density,

where B is the magnetic field and D the electric displacement field.
The first term in the right-hand side represents the net electromagnetic energy flow into a small volume, while the second term represents the subtracted portion of the work done by free electrical currents that are not necessarily converted into electromagnetic energy (dissipation, heat). In this definition, bound electrical currents are not included in this term, and instead contribute to S and u.
Note that u can only be given if linear, nondispersive and uniform materials are involved, i.e., if the constitutive relations can be written as

where ε and μ are constants (which depend on the material through which the energy flows), called the permittivity and permeability, respectively, of the material.
This practically limits Poynting's theorem in this form to fields in vacuum. A generalization to dispersive materials is possible under certain circumstances at the cost of additional terms and the loss of their clear physical interpretation.
2. FORMULATION IN TERMS OF MICROSCOPIC FIELDS
In some cases, it may be more appropriate to define the Poynting vector as

where μ0 is the magnetic constant. It can be derived directly from Maxwell's equations in terms of total charge and current and the Lorentz force law only.
The corresponding form of Poynting's theorem is

where is the total current density and the energy density u is

(with the electric constant ε0).
The two alternative definitions of the Poynting vector are equivalent in vacuum or in non-magnetic materials, where . In all other cases, they differ in that and the corresponding u are purely radiative, since the dissipation term, , covers the total current, while the definition in terms of has contributions from bound currents which then lack in the dissipation term.
Since only the microscopic fields and are needed in the derivation of , assumptions about any material possibly present can be completely avoided, and Poynting's vector as well as the theorem in this definition are universally valid, in vacuum as in all kinds of material. This is especially true for the electromagnetic energy density, in contrast to the case above.
3. INVARIANCE TO ADDING A CURL OF A FIELD
Since the Poynting vector only occurs in Poynting's theorem as a divergence , the Poynting vector is arbitrary to the extent that the curl of any field F can be added, because for any field. Doing so is not common, though, and will lead to inconsistencies in a relativistic description of electromagnetic fields in terms of the stress-energy tensor.
4. EXAMPLES AND APPLICATIONS
 The Poynting vector in a coaxial cable
For example, the Poynting vector within the dielectric insulator of a coaxial cable is nearly parallel to the wire axis (assuming no fields outside the cable) - so electric energy is flowing through the dielectric between the conductors. If the core conductor was replaced by a wire having significant resistance, then the Poynting vector would become tilted toward that wire, indicating that energy flows from the electromagnetic field into the wire, producing resistive Joule heating in the wire.
 The Poynting vector in plane waves
In a propagating sinusoidal electromagnetic plane wave of a fixed frequency, the Poynting vector oscillates, always pointing in the direction of propagation. The time-averaged magnitude of the Poynting vector is

where is the maximum amplitude of the electric field and is the speed of light in free space. This time-averaged value is also called the irradiance or intensity I.
5. DERIVATION
In an electromagnetic plane wave, and are always perpendicular to each other and the direction of propagation. Moreover, their amplitudes are related according to

and their time and position dependences are


where is the frequency of the wave and is wave vector. The time-dependent and position magnitude of the Poynting vector is then

In the last step, we used the equality . Since the time- or space-average of is ½, it follows that

 Poynting vector and radiation pressure
S divided by the square of the speed of light in free space is the density of the linear momentum of the electromagnetic field. The time-averaged intensity divided by the speed of light in free space is the radiation pressure exerted by an electromagnetic wave on the surface of a target:






BLACK BODY RADIATION












1. DEFINES
Black body spectrum the spectral distribution of energy in the temperature of the body. The higher the temperature, the greater the amount of radiation and the higher the frequency at which true maximum the maximum emission occurs.
As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.

The color (chromaticity) of black-body radiation depends on the temperature of the black body; the locus of such colors, shown here in CIE 1931 x,y space, is known as the Planckian locus.
In physics, a black body is an idealized object that absorbs all electromagnetic radiation that falls on it. No electromagnetic radiation passes through it and none is reflected. Because no light (visible electromagnetic radiation) is reflected or transmitted, the object appears black when it is cold. However, a black body emits a temperature-dependent spectrum of light. This thermal radiation from a black body is termed black-body radiation.
At room temperature, black bodies emit mostly infrared wavelengths, but as the temperature increases past a few hundred degrees Celsius, black bodies start to emit visible wavelengths, appearing red, orange, yellow, white, and blue with increasing temperature. By the time an object is white, it is emitting substantial ultraviolet radiation. The term "black body" was introduced by Gustav Kirchhoff in 1860.
2. EXPLANATION

A typical industrial "extended
source plate" type black body.






Black-body radiation is light in thermal equilibrium with a black body, light radiation with a given temperature. It is the reference thermodynamic equilibrium state of light. Experimentally, it is established as the steady state equilibrium radiation in a rigid-walled cavity that contains a black body. There are no strictly exact black bodies in nature, but graphite is a good approximation, and a closed box with graphite walls at a steady state gives a good approximation to ideal black body radiation. A cavity that does not contain any black material body does not sustain black body radiation at equilibrium; this fact was found experimentally by Kirchhoff but its physical significance was understood neither by Kirchhoff nor by Planck.
Because light is the oscillation of a continuous electromagnetic field, the study of black-body radiation reveals how continuous fields can have a temperature, something which contradicts classical physics. Because the thermal state of light was so confusing before the advent of quantum mechanics, the 19th century arguments that light has a thermal equilibrium state were made very carefully.
An object at some fixed temperature T, like an oven, is observed to glow. The Draper point is the name given to the point at which all solids glow a dim red (about 798 K). At 1000 K, an oven looks red; at 6000 K, it looks white. No matter how the oven is constructed, so long as the oven is not too shiny, the color of the light only depends on the temperature. Since color is the directly visible measure of the wavelength, this observation means that light at different temperatures has a different distribution of energy among the different wavelengths. The amount of energy E per unit volume in wavelength λ at temperature T is called the black-body curve. Detailed experiments revealed that the black-body curve only depends on the temperature, not on the emitting body. This suggests that light does in fact come to thermal equilibrium just like anything else, that the concept of light at temperature T makes sense.
When the body is black, the absorption is obvious: the amount of light absorbed is all the light that hits the surface. For a black body much bigger than the wavelength, the light energy absorbed at any wavelength λ per unit time is strictly proportional to the black-body curve. This means that the black-body curve is the amount of light energy emitted by a black body, which justifies the name. This is Kirchhoff's law of thermal radiation: the black-body emission curve is a thermal characteristic of light, which depends only on the temperature of the walls of the cavity, provided strictly that the cavity contains some perfectly black material body and is in radiative equilibrium.
The wavelength at which the radiation is strongest is given by Wien's displacement law, and the overall power emitted per unit area is given by the Stefan-Boltzmann law. So, as temperature increases, the glow color changes from red to yellow to white to blue. Even as the peak wavelength moves into the ultra-violet, enough radiation continues to be emitted in the blue wavelengths that the body will continue to appear blue. It will never become invisible—indeed, the radiation of visible light increases monotonically with temperature.
When dealing with non-black surfaces, the deviations from ideal black-body behavior are determined by both the geometrical structure and the chemical composition, and, provided there is a radiative equilibrium with a nearly black body that is present, nearly follow Kirchhoff's Law: emissivity equals absorptivity, so that an object that does not absorb all incident light will also emit less radiation than an ideal black body.


3. EQUATIONS GOVERNING BLACK BODIES
 Planck's law of black-body radiation
Electromagnetic radiation has particle-like properties as discrete packets of energy, or quanta, called photons. The frequency of the wave is proportional to the particle's energy. Because photons are emitted and absorbed by charged particles, they act as transporters of energy. The energy per photon can be calculated from the Planck–Einstein equation:

Planck's law states that

Where:
I(ν,T) dν is the amount of energy per unit surface area per unit time per unit solid angle emitted in the frequency range between ν and ν + dν by a black body at temperature T;
h is the Planck constant;
c is the speed of light in a vacuum;
k is the Boltzmann constant;
ν is frequency of electromagnetic radiation; and
T is the temperature in kelvins.

 Wien's displacement law
Wien's displacement law shows how the spectrum of black body radiation at any temperature is related to the spectrum at any other temperature. If we know the shape of the spectrum at one temperature, we can calculate the shape at any other temperature.
A consequence of Wien's displacement law is that the wavelength at which the intensity of the radiation produced by a black body is at a maximum, λmax, it is a function only of the temperature:

Where the constant, b, known as Wien's displacement constant, is equal to 2.8977685(51)×10−3 m K.
Note that the peak intensity can be expressed in terms of intensity per unit wavelength or in terms of intensity per unit frequency. The form given in this section is in terms of intensity per unit wavelength, this form given in the Planck's Law section above was in terms of intensity per unit frequency. The wavelength at which the power per unit frequency is maximised is given by
.
 Stefan–Boltzmann law
This law states that amount of thermal radiation emitted per second per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature. That is

Where j* is the total energy radiated per unit area per unit time, T is the temperature in kelvins, and σ = 5.67×10−8 W m−2 K−4 is the Stefan–Boltzmann constant.