## What is electromagnetic power density?

The power density of an electromagnetic (EM) wave is proportional to the square of the frequency of electric field (or magnetic field). The moving charge produces both electric field and magnetic field. Electric and magnetic fields are inseparable and exist in combination in EM waves.

## What is the principle of electromagnetic power density?

When an electromagnetic wave propagates towards a source, it transmits energy to the elements along its path. The electromagnetic wave stores energy in electric and magnetic fields. The amount of energy stored in electric waves is equal to the amount of energy stored in electric and magnetic fields. In that case, the energy density of the wave is the sum of the density of the electric field and the density of the magnetic field.

Electromagnetic radiation contains perpendicular oscillations of electric and magnetic fields. Electromagnetic radiation or electromagnetic waves are caused by periodical modifications of the electric or magnetic fields.

## Electromagnetic force

Electromagnetic force is a form of physical interaction that takes place between charged particles. It works between charged particles and is a combination of all magnetic and electrical energy. Electromagnetic force can be attractive or it can be repulsive.

Before the discovery of electromagnetism, people or scientists thought that electricity and magnetism were two separate topics. Opinion changed after James Clerk Maxwell published his book A Treatise on Electricity and Magnetism in 1873. The book suggests that the combination of positive and negative charges intervenes strongly. This view laid the foundation for Electromagnetism. Many scientists such as Michael Faraday, Oliver Heaviside, and Heinrich Hertz later offered their ideas on the magnetic field.

Electromagnetism is the process of generating a magnetic field by passing a current through a conductor. For example, if at any instantaneous time, an alternating current flows through a wire, a magnetic field is generated near the wire, and the direction of the magnetic field and force can be determined using the right-hand rule.

Electromagnetic waves are formed when an electric field meets a magnetic field. They are therefore known as electromagnetic waves. The electric field and the electromagnetic wave are perpendicular to each other. They also flows in the direction of the electromagnetic waves. EM waves carry energy, momentum, and angular moment away from their source particles and may transmit the same amount of matter to which they interact. Electromagnetic radiation is associated with those electromagnetic EM waves that can be free to radiate without the continuous effect of the moving charge they produce, as they reach a considerable distance from those charges.

## Power density

Power density is the rate of energy output per volume of each unit. Although it is not the most widely used measure of energy density, it is still useful in discussions about energy systems (usually in portable services such as transportation). It helps to understand the energy density of the energy versus the energy density.

The system has a large capacity, rather than being able to produce large amounts of energy based on its capacity. For example, a small capacitor may have the same power as a large battery. Because the capacitor is very small, it has a large power supply. As it releases its power quickly, high-density systems can also be charged faster.

In electromagnetism, a complete clearance, commonly called permittivity and is defined by the Greek letter ε (epsilon), is a measure of dielectric electric current. In electromagnetic light intensity is equal to frequency and is inverse proportional to its length. The proportionality constant is known as Planck's constant *h*. It is to be noted that an electromagnetic wave is not made of photons.

## Energy density of EM wave

Consider a magnetic field that travels in a relaxed atmosphere in a positive x-axis direction. The electric field associated with the wave changes in the y-direction and the magnetic field alternates in the z-direction. Let the electric and magnetic fields be mathematically represented in cosine form:

${E}_{y}\left(x,t\right)={E}_{0}\mathrm{cos}\left(kx-\omega t\right)\phantom{\rule{0ex}{0ex}}{B}_{z}\left(x,t\right)={B}_{0}\mathrm{cos}\left(kx-\omega t\right)$

The energy stored in any part of an electric wave is the sum of the electrical energy density and the magnetic field. The amount of energy stored per unit volume is the amount of electrical energy (U), which is the total amount of electrical energy (U_{E}) and the energy density of the magnetic field (U_{B}).

The generalization of phenomenological equations for electromagnetic field in superconductor is based on algebraic space-time equations.

The definition of a magnetic field density, in which 𝜇_{0} is free space and 𝜺_{0} is free space is shown below. Note that the unit for density is $\mathrm{J}/{\mathrm{m}}^{3}$:

$U={U}_{B}+{U}_{E}=\frac{1}{2}\left(\frac{1}{{\mu}_{0}}{B}^{2}+{\epsilon}_{0}{E}^{2}\right)$

## What is a Poynting vector in an electromagnetic field?

Poynting vector, a range that describes the magnitude and direction of the charge with the flow of power in an electric field. It is known after the English physicist John Henry Poynting, who added it in 1884.

Poynting vector S is defined as the equivalent of the opposite product $\frac{E\times B}{\mu}$, where $\mu $ is the intensity of the radiation, E is the length of the electric field, and B the length of the magnetic field. The use of product description (see vector) and information of the electrical and magnetic fields of the others give the S value of the vector in Poynting as $\frac{E\times B}{\mu}$, where E and B, respectively, are magnitude of vectors, E and B. Product direction of vector S depends on the path determined by vectors E and B. To detect the motion of a moving electromagnetic wave, the Poynting vector indicates where the wave is propagating. In simple terms, the Poynting vector S indicates the direction and degree of power transfer, solid, due to the magnetic fields in the space which may be empty.

## Common Mistakes

Remember that, electromagnetic waves heat up very quickly and as a result of this heat generation the energy losses are very high.

## Context and Applications

In each of the expert exams for undergraduate and graduate publications, this topic is huge and is mainly used for:

- Bachelor of technology in the electrical and electronic department
- Bachelor of Science in physics
- Master of Science in physics

## Related Concepts

Electromagnetic radiation

## Practice Problems

**Q1**. Dimensions of pointing vector p, are same as that of___________.

- Power
- Power/Area
- Volt/Meter
- Meter

**Correct option:** (b)

**Explanation:** Pointing vector s is equal to the ratio of electric field and magnetic field.

It can be written as, equation form $S=\frac{Power}{Area}$

**Q2.** The power in a wave given that H component is 0.82 units in air___________.

- 126.74
- 621.47
- 216.47
- 745.62

**Correct option:** (a)

**Explanation:** The equation of power wave is given by $P=\frac{\eta {H}^{2}}{2}$.

In air medium, $\eta =377$ and given that $H=0.82$. And substitute the value in the equation.

From the equation the power is:

$P=\frac{377\times 0.{82}^{2}}{2}\phantom{\rule{0ex}{0ex}}P=126.74\mathrm{units}$.

**Q3.** The power of a wave with electric field intensity of 3 units in air is___________.

- 0.02
- 0.03
- 0.01
- 0.04

**Correct option:** (c)

**Explanation:** The Poynting vector gives the power of a wave.

It is given as $P=\frac{{E}^{2}}{2\eta}$.

On substituting in the equation $E=3$ and $\eta =377$ air,

From the equation the power is

$P=\frac{{3}^{2}}{2\times 377}\phantom{\rule{0ex}{0ex}}P=0.01\mathrm{units}$

**Q4.** The power per unit area velocity of a wave with the electric field as 8 units and density of 10 units is___________.

- 40
- 20
- 80
- 160

**Correct option:** (c)

**Explanation:** The power per unit velocity $\frac{P}{V}$ is given by the product of the electric field and the density. From equation:

$\frac{P}{v}=E.d=8\times 10=80\mathrm{units}$

**Q5.** The total power of a wave with average power 15 units in a surface density of 0.5 units is___________.

- 4.87
- 2.0
- 7.5
- 1.60

**Correct option:** (c)

**Explanation:** The total power is given by the surface integral of the average power. This equation $\int {P}_{avg}gds$ is the total power. On substituting in the equation ${P}_{avg}=15$ and and $\int ds=0.5$ get total power as 7.5 units.

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