# plane electromagnetic wave in free space Dobbs 1 1. University of London UK. Personalised recommendations. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B , takes the form:. In most older literature, B is called the magnetic flux density or magnetic induction. In Part VI of his paper titled Electromagnetic Theory of Light ,  Maxwell combined displacement current with some of the other equations of electromagnetism and he obtained a wave equation with a speed equal to the speed of light.

He commented:. The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws. To obtain the electromagnetic wave equation in a vacuum using the modern method, we begin with the modern ' Heaviside' form of Maxwell's equations.

In a vacuum- and charge-free space, these equations are:. These are the general Maxwell's equations specialized to the case with charge and current both set to zero. Taking the curl of the curl equations gives:. We can use the vector identity. If the radiation is reflected instead of absorbed, then its momentum changes direction.

The radiation pressure on an object that reflects the radiation is therefore twice the radiation pressure on an object that absorbs the radiation. Electromagnetic waves transport energy and momentum across space. The energy and momentum transported by an electromagnetic wave are not continuously distributed over the wave front. Energy and momentum are transported by photons in discrete packages.

Photons are the particles of light. Light is "quantized". Photons always move with the speed of light. So what is an electromagnetic wave, a wave or a stream of photons? What is our current understanding of the nature of light and other EM waves? Quantum mechanics views photons as quanta or packets of energy. Imagine the excitement that Maxwell must have felt when he discovered this equation! He had found a fundamental connection between two seemingly unrelated phenomena: electromagnetic fields and light.

These quantities are related in the same way as for a mechanical wave:. This means that a relatively strong electric field of is accompanied by a relatively weak magnetic field. Changing electric fields create relatively weak magnetic fields.

The combined electric and magnetic fields can be detected in electromagnetic waves, however, by taking advantage of the phenomenon of resonance, as Hertz did. A system with the same natural frequency as the electromagnetic wave can be made to oscillate. All radio and TV receivers use this principle to pick up and then amplify weak electromagnetic waves, while rejecting all others not at their resonant frequency. A steady electric current produces a magnetic field that is constant in time and which does not propagate as a wave.

Accelerating charges, however, produce electromagnetic waves. The electromagnetic wave is therefore a transverse wave, with its oscillating electric and magnetic fields perpendicular to its direction of propagation.

We then combine the two equations to show how the changing E and B fields propagate through space at a speed precisely equal to the speed of light. The flux of the B field through Face 3 is then the B field times the area,. This is the equation describing the spatially dependent E field produced by the time-dependent B field.

Applying Equation These equations describe the spatially dependent B field produced by the time-dependent E field. We next combine the equations showing the changing B field producing an E field with the equation showing the changing E field producing a B field. This is the form taken by the general wave equation for our plane wave. The speed of the electromagnetic wave in free space is therefore given in terms of the permeability and the permittivity of free space by. The physics of traveling electromagnetic fields was worked out by Maxwell in Imagine the excitement that Maxwell must have felt when he discovered this equation!

He had found a fundamental connection between two seemingly unrelated phenomena: electromagnetic fields and light. The wave equation was obtained by 1 finding the E field produced by the changing B field, 2 finding the B field produced by the changing E field, and combining the two results.

So far, we have seen that the rates of change of different components of the E and B fields are related, that the electromagnetic wave is transverse, and that the wave propagates at speed c.

Basic Electromagnetism pp Cite as. Electromagnetic fields propagate in space, in dielectrics and, to a limited extent, in plasmas and conductors. Unable to display preview. Download preview PDF. Dave to main content. This service is more plane electromagnetic wave in free space with JavaScript available. Advertisement Hide. Electromagnetic waves in space. Authors Authors and affiliations E. This process is experimental and the plane electromagnetic wave in free space may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Dobbs 1 1. University of London UK. Personalised recommendations. Cite chapter How to cite? ENW EndNote. Buy options. Electromagnetic wave equation in free space. • Uniform plane wave solutions of the wave equation. • Energy and power of electromagnetic waves. ECE We can, however, investigate the special case of an electromagnetic wave that propagates through free space along the x-axis of a given. A similar derivation gives the same equation for B. Now let's look at a plane wave solution: A wave guide is a region with a conducting boundary inside which EM waves are caused This equation is the same as we obtained for free space. EM waves require no medium, they can travel through empty space. Sinusoidal plane directions. A plane EM wave traveling in the x-direction is of the form. The electromagnetic wave equation is a second-order partial differential equation that In a vacuum- and charge-free space, these equations are: Main article: Sinusoidal plane-wave solutions of the electromagnetic wave equation. Start with Maxwell's equations in derivative form for empty space. The electric field describes an electromagnetic wave completely in free space. The magnetic​. We can, however, investigate the special case of an electromagnetic wave that propagates through free space along the x-axis of a given coordinate system. A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E=6​. A plane electromagnetic wave travels in free space along X-direction. If the value of B (in tesla) at a particular point in space and time is. Because Maxwell's equations hold in free space, the predicted electromagnetic waves, unlike mechanical waves, do not require a medium for their propagation. Philosophical Transactions of the Royal Society of London. Help Community portal Recent changes Upload file. But as the permeability and permittivity values are different then expression in both cases gets varied. It is not a coincidence that this happens in the visible range, as the mechanism of vision involves the change in bonding of a single molecule retinal which absorbs light in the rhodopsin in the retina of the human eye. EM radiation exhibits both wave properties and particle properties at the same time see wave-particle duality. Earth's energy budget Electromagnetic radiation Synchrotron radiation Thermal radiation Black-body radiation Particle radiation Gravitational radiation Cosmic background radiation Cherenkov radiation Askaryan radiation Bremsstrahlung Unruh radiation Dark radiation. One of these anomalies involved a controversy over the speed of light. Whereas the magnetic part of the near-field is due to currents in the source, the magnetic field in EMR is due only to the local change in the electric field. It can efficiently launch and receive electromagnetic waves. Such a representation is called the power spectral density of the random process. Lower frequencies have longer wavelengths, and higher frequencies have shorter wavelengths, and are associated with photons of higher energy. Such effects can cover macroscopic distances in conductors such as radio antennas , since the wavelength of radiowaves is long. Frequency Range Hz. 