Surface power density

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In physics and engineering, surface power density is power per unit area.

Contents

Applications

Surface power densities of energy sources

Surface power density is an important factor in comparison of industrial energy sources. [1] The concept was popularised by geographer Vaclav Smil. The term is usually shortened to "power density" in the relevant literature, which can lead to confusion with homonymous or related terms.

Measured in W/m2 it describes the amount of power obtained per unit of Earth surface area used by a specific energy system, including all supporting infrastructure, manufacturing, mining of fuel (if applicable) and decommissioning. [2] , [3] Fossil fuels and nuclear power are characterized by high power density which means large power can be drawn from power plants occupying relatively small area. Renewable energy sources have power density at least three orders of magnitude smaller and for the same energy output they need to occupy accordingly larger area, which has been already highlighted as a limiting factor of renewable energy in German Energiewende. [4]

The following table shows median surface power density of renewable and non-renewable energy sources. [5]

Energy sourceMedian PD

[W/m2]

Fossil gas 482.10
Nuclear power 240.81
Oil194.61
Coal135.10
Solar power 6.63
Geothermal2.24
Wind power 1.84
Hydropower 0.14
Biomass 0.08

Background

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). [6]


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. [6]

The above equation yields units of W/m2 . In the USA 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: [6]

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. [6]

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. [??? This would imply that with no absorption, E and H are both zero, i.e. light or radio waves cannot travel in a vacuum. The intended meaning of this statement is unclear.] [6]

Far field

The region extending farther than about 2 wavelengths away from the source is called the far field. As the source emits electromagnetic radiation of a given wavelength, the far-field electric component of the wave E, the far-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. [6]

Related Research Articles

The gauss, is a unit of measurement of magnetic induction, also known as magnetic flux density. The unit is part of the Gaussian system of units, which inherited it from the older centimetre–gram–second electromagnetic units (CGS-EMU) system. It was named after the German mathematician and physicist Carl Friedrich Gauss in 1936. One gauss is defined as one maxwell per square centimetre.

<span class="mw-page-title-main">Magnetic field</span> Spatial distribution of vectors allowing the calculation of the magnetic force on a test particle

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field.

In physics, the intensity or flux of radiant energy is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units watts per square metre (W/m2), or kg⋅s−3 in base units. Intensity is used most frequently with waves such as acoustic waves (sound) or electromagnetic waves such as light or radio waves, in which case the average power transfer over one period of the wave is used. Intensity can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler.

Flux describes any effect that appears to pass or travel through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface.

<span class="mw-page-title-main">Poynting vector</span> Measure of directional electromagnetic energy flux

In physics, the Poynting vector represents the directional energy flux or power flow of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m2); kg/s3 in base SI units. It is named after its discoverer John Henry Poynting who first derived it in 1884. Nikolay Umov is also credited with formulating the concept. Oliver Heaviside also discovered it independently in the more general form that recognises the freedom of adding the curl of an arbitrary vector field to the definition. The Poynting vector is used throughout electromagnetics in conjunction with Poynting's theorem, the continuity equation expressing conservation of electromagnetic energy, to calculate the power flow in electromagnetic fields.

<span class="mw-page-title-main">Magnet</span> Object that has a magnetic field

A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, cobalt, etc. and attracts or repels other magnets.

The oersted is the coherent derived unit of the auxiliary magnetic field H in the centimetre–gram–second system of units (CGS). It is equivalent to 1 dyne per maxwell.

<span class="mw-page-title-main">Electromagnet</span> Magnet created with an electric current

An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in the hole in the center of the coil. The magnetic field disappears when the current is turned off. The wire turns are often wound around a magnetic core made from a ferromagnetic or ferrimagnetic material such as iron; the magnetic core concentrates the magnetic flux and makes a more powerful magnet.

<span class="mw-page-title-main">Radio wave</span> Type of electromagnetic radiation

Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz (GHz) and below. At 300 GHz, the corresponding wavelength is 1mm, which is shorter than the diameter of a grain of rice. At 30 Hz the corresponding wavelength is ~10,000 kilometers, which is longer than the radius of the Earth. Wavelength of a radio wave is inversely proportional to its frequency, because its velocity is constant. Like all electromagnetic waves, radio waves in a vacuum travel at the speed of light, and in the Earth's atmosphere at a slightly slower speed. Radio waves are generated by charged particles undergoing acceleration, such as time-varying electric currents. Naturally occurring radio waves are emitted by lightning and astronomical objects, and are part of the blackbody radiation emitted by all warm objects.

<span class="mw-page-title-main">Near and far field</span> Regions of an electromagnetic field

The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative near-field behaviors dominate close to the antenna or scatterer, while electromagnetic radiation far-field behaviors predominate at greater distances.

In physics, the weber is the unit of magnetic flux in the International System of Units (SI), whose units are volt-second. A magnetic flux density of one Wb/m2 is one tesla.

<span class="mw-page-title-main">Radar cross section</span> Strength of an objects radar echo

Radar cross-section (RCS), denoted σ, also called radar signature, is a measure of how detectable an object is by radar. A larger RCS indicates that an object is more easily detected.

The tesla is the unit of magnetic flux density in the International System of Units (SI).

<span class="mw-page-title-main">Magnetization</span> Physical quantity, density of magnetic moment per volume

In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quantity of magnetic moment per unit volume. It is represented by a pseudovector M. Magnetization can be compared to electric polarization, which is the measure of the corresponding response of a material to an electric field in electrostatics.

In electromagnetics, the antenna factor is defined as the ratio of the electric field E to the voltage V induced across the terminals of an antenna:

Intensity may refer to:

<span class="mw-page-title-main">Electric power</span> Rate at which electrical energy is transferred by an electric circuit

Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions of watts are called kilowatts, megawatts and gigawatts respectively.

A high-intensity radiated field (HIRF) is radio-frequency energy of a strength sufficient to adversely affect either a living organism or the performance of a device subjected to it. A microwave oven is an example of this principle put to controlled, safe use. Radio-frequency (RF) energy is non-ionizing electromagnetic radiation – its effects on tissue are through heating. Electronic components are affected via rectification of the RF and a corresponding shift in the bias points of the components in the field.

Magnets exert forces and torques on each other through the interaction of their magnetic fields. The forces of attraction and repulsion are a result of these interactions. The magnetic field of each magnet is due to microscopic currents of electrically charged electrons orbiting nuclei and the intrinsic magnetism of fundamental particles that make up the material. Both of these are modeled quite well as tiny loops of current called magnetic dipoles that produce their own magnetic field and are affected by external magnetic fields. The most elementary force between magnets is the magnetic dipole–dipole interaction. If all magnetic dipoles for each magnet are known then the net force on both magnets can be determined by summing all the interactions between the dipoles of the first magnet and the dipoles of the second magnet.

References

  1. "Nature Energy and Society: A scientific study of the options facing civilisation today". ResearchGate. Retrieved 2020-07-23.
  2. Smil, Vaclav (May 2015). Power Density: A Key to Understanding Energy Sources and Uses. MIT Press. ISBN   9780262029148 . Retrieved 2023-09-12.
  3. Smil, Vaclav (May 8, 2010). "Power Density Primer: Understanding the Spatial Dimension of the Unfolding Transition to Renewable Electricity Generation (Part I – Definitions)" (PDF). Master Resource, A Free Market Energy Blog. Retrieved September 18, 2019.
  4. "Land set to become "new currency" of Germany's energy transition – study". Clean Energy Wire. Retrieved 2021-10-05.
  5. van Zalk, John; Behrens, Paul (2018-12-01). "The spatial extent of renewable and non-renewable power generation: A review and meta-analysis of power densities and their application in the U.S." Energy Policy. 123: 83–91. doi: 10.1016/j.enpol.2018.08.023 . ISSN   0301-4215.
  6. 1 2 3 4 5 6 OSHA, Cincinnati Technical Center (May 20, 1990). "Electromagnetic Radiation and How It Affects Your Instruments. Units" (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 referenced work). U.S. Dept of Labor. Retrieved 2010-05-09.{{cite web}}: External link in |format= (help)