Explicit formulae (L-function)

2014-01-06T05:20:28Z

192.153.105.136: /* Weil's explicit formula */

{{Refimprove|date=June 2006}}

In [[physics]] and [[engineering]], '''surface power density''' or sometimes simply '''specific power'''<ref>[http://physics.nist.gov/Pubs/SP811/sec04.html]</ref> is [[power (physics)|power]] per unit [[area]].

==Applications==
* The intensity of [[electromagnetic waves|electromagnetic radiation]] can be expressed in W/m2. An example of such a quantity is the [[solar constant]].
* [[Wind turbine]]s are often compared using a specific power measuring watts per [[square meter]] of turbine disk area, which is <math>\pi r^{2}</math>, where ''r'' is the length of a blade. This measure is also commonly used for [[Photovoltaic module|solar panel]]s, at least for typical applications.
* [[Radiance]] is surface power density per unit of solid angle (steradians) in a specific direction. [[Spectral radiance]] is radiance per unit of frequency (Hertz) at a specific frequency.

===Electromagnetic wave===
As an electromagnetic wave travels through space, energy is transferred from the source to other objects (receivers). The rate of this energy transfer depends on the strength of the EM field components. Simply put, the rate of energy transfer per unit area (power density) is the product of the electric field strength (E) times the magnetic field strength (H).<ref name=OSHA-Pwr-density/>

:Pd (Watts/meter2) = E × H (Volts/meter × Amperes/meter)
where
:Pd = the power density,
:E = the RMS electric field strength in volts per meter,
:H = the RMS magnetic field strength in amperes per meter.<ref name=OSHA-Pwr-density/>

The above equation yields units of W/m2 . The units of mW/cm2, are more often used when making surveys. One mW/cm2 is the same power density as 10 W/m2. The following equation can be used to obtain these units directly:<ref name=OSHA-Pwr-density/>

:Pd = 0.1 × E × H mW/cm2

The simplified relationships stated above apply at distances of about two or more wavelengths from the radiating source. This distance can be a far distance at low frequencies, and is called the far field. Here the ratio between E and H becomes a fixed constant (377 Ohms) and is called the [[characteristic impedance of free space]]. Under these conditions we can determine the power density by measuring only the E field component (or H field component, if you prefer) and calculating the power density from it.<ref name=OSHA-Pwr-density/>

This fixed relationship is useful for measuring radio frequency or microwave (electromagnetic) fields.Since power is the rate of energy transfer, and the squares of E and H are proportional to power, E2 and H2 are proportional to the energy transfer rate and the energy absorption of a given material.<ref name=OSHA-Pwr-density>
{{Cite web
| last =OSHA| first =Cincinnati Technical Center| title =Electromagnetic Radiation and How It Affects Your Instruments. Units. | publisher =U.S. Dept of Labor| date =May 20, 1990
| url=http://www.osha.gov/SLTC/radiofrequencyradiation/electromagnetic_fieldmemo/electromagnetic.html#section_2| format =Department of Labor - Public Domain content. Most of the content referenced by this work in this article is copied from a public domain document. In addition, this paper is a
[http://www.osha.gov/SLTC/radiofrequencyradiation/electromagnetic_fieldmemo/electromagnetic.html#reference_x referenced work]| accessdate =2010-05-09}}</ref>

====Far field====

The region extending farther than about 2 [[wavelength]]s away from the source is called the [[far field]]. As the source emits [[electromagnetic radiation]] of a given wavelength, the far-field [[electric field|electric component]] of the wave '''''E''''', the far-field [[magnetic field|magnetic component]] '''''H''''', and '''''power density''''' are related by the equations: E = H × 377 and Pd = E × H.

:Pd = H2 × 377 and Pd = E2 ÷ 377
::where Pd is the power density in watts per square meter (one W/m2 is equal to 0.1 mW/cm2),
::H2 = the square of the value of the magnetic field in amperes RMS squared per meter squared,
::E2 = the square of the value of the electric field in volts RMS squared per meter squared.<ref name=OSHA-Pwr-density/>

==References==
{{Reflist}}

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Explicit formulae (L-function)