physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

and

engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...

, surface power density is power per unit

area Area is the measure of a region's size on a surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an open surface or the boundary of a three-di ...

Applications

* The

intensity Intensity may refer to: In colloquial use * Strength (disambiguation) *Amplitude * Level (disambiguation) * Magnitude (disambiguation) In physical sciences Physics *Intensity (physics), power per unit area (W/m2) *Field strength of electric, m ...

electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...

can be expressed in W/m². An example of such a quantity is the solar constant. *

Wind turbine A wind turbine is a device that wind power, converts the kinetic energy of wind into electrical energy. , hundreds of thousands of list of most powerful wind turbines, large turbines, in installations known as wind farms, were generating over ...

s are often compared using a specific power measuring watts per

square meter The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square w ...

of turbine disk area, which is

\pi r^

, where ''r'' is the length of a blade. This measure is also commonly used for

solar panel A solar panel is a device that converts sunlight into electricity by using photovoltaic (PV) cells. PV cells are made of materials that produce excited electrons when exposed to light. These electrons flow through a circuit and produce direct ...

s, at least for typical applications. *

Radiance In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiati ...

is surface power density per unit of solid angle (steradians) in a specific direction.

Spectral radiance In radiometry, spectral radiance or specific intensity is the radiance of a surface per unit frequency or wavelength, depending on whether the Spectral radiometric quantity, spectrum is taken as a function of frequency or of wavelength. The Interna ...

is radiance per unit of frequency (Hertz) at a specific (or as a function of) frequency, or per unit of wavelength (e.g. nm) at a specific (or as a function of) wavelength.

Surface power densities of energy sources

Surface power density is an important factor in comparison of industrial energy sources. 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 An energy system is a system primarily designed to supply #Energy-services, energy-services to end user, end-users. The intent behind energy systems is to minimise energy losses to a negligible level, as well as to ensure the efficient use of ...

, including all supporting infrastructure, manufacturing, mining of fuel (if applicable) and decommissioning.^, 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 Renewable energy (also called green energy) is energy made from renewable resource, renewable natural resources that are replenished on a human lifetime, human timescale. The most widely used renewable energy types are solar energy, wind pow ...

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

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). :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. 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: :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. 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.

Far field

The region extending farther than about 2

wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

s away from the source is called the far field. As the source emits

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.

References

{{Authority control Physical quantities Area-specific quantities