# 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 , [2] 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.