# A wave that is out of phase with itself

A wave that is out of phase
with itself

23 August 2012

I do not think such wave exists. The electricand magnetic fields of plan wave are in phase. But that of the solution of theEM wave equation are out of phase. In the Figure1, an element of antenna emits a wave composed ofelectric field E and magnetic field H. The phase of the electric and magnetic fields vary differently, so the electric field wave slides with respect to the magnetic field wave. For example, if the maximums of the 2 fields coincide at a point r1, a moment later, each will travel a different distance and the 2 will separate. In other words, the wave in terms of electric field is out of phase with itself in terms of magnetic field.

at blogspot

# Can EM wave go forward back?

Can EM wave go forward back?
19 August 2012

This is a bizarre question, but the solution of the EM wave equation goes this way. Take an element of antenna in which an alternate current emits a wave, as shown in the Figure 1. The electric field of this wave is given by the equations (1). Strangely, v is negative for small distance. This is non sense because real waves travel forward, from antenna into space. This is why I said “EM wave goes forward back”.

Can EM wave go forward back?
or
http://pengkuanem.blogspot.com/2012/08/can-em-wave-go-forward-back.html

### Aside

Summary

Theory about displacement current and wave

Why EM wave equation does not conform to relativity?
http://pengkuanem.blogspot.com/2012/08/why-em-wave-equation-does-not-conform.html

Comparison of the 2 magnetic force laws
http://pengkuanem.blogspot.com/2012/05/comparison.html

Correct differential magnetic force law
http://pengkuanem.blogspot.com/2012/04/correct-law.html

Synthesis of the inconsistency of the Lorentz force law
http://pengkuanem.blogspot.com/2012/04/synthesis.html

Mathematical cause of the existence of the remaining resultant internal Lorentz force (near a corner, force tends to infinity)
http://pengkuanem.blogspot.com/2012/04/mathematical-cause-of-existence-of.html

Proof of the remaining resultant Lorentz force internal to a triangular coil (integration of resultant force)
http://pengkuanem.blogspot.com/2012/04/analyze-of-lorentz-forces-internal-to.html

http://pengkuanem.blogspot.com/2012/04/complete-study.html

Analyze of the Lorentz forces internal to an equilateral triangle coil (magnetic shield)
http://pengkuanem.blogspot.com/2012/03/lorentz-forces-internal-to-equilateral.html

Lorentz forces internal to a polygon coil, analyze and computation
http://pengkuanem.blogspot.com/2012/03/lorentzforce-internal-to-coil-analyze.html

Experiment designs and computation about Lorentz force law

Calculation of the Lorentz’ Torque and the Ampere’s torque
http://pengkuanem.blogspot.com/2012/05/torque-calculation.html

Experiment designs about displacement current and wave

# Why EM wave equation does not conform to relativity?

Why EM wave equation does not conform to relativity?
1 August 2012

This question is not about real electromagnetic wave. Physical wave does not violate relativity principle and always travel at constant speed c. It is the electromagnetic wave equation that does not conform to relativity. By computing the speed of the solution of the wave equation, we find that its velocity is faster than that of light and varies with distance and frequency. This result proves that the wave equation does not faithfully describe the physical phenomenon of electromagnetic wave.

A rigorous mathematical proof is given below. The annex is provided just in case where someone wants to check the validity of the used equations and is not necessary to the proof.

We study the spherical wave sent by an element of antenna of length dl which carries a current I (see the Figure 1). As the magnetic field of this element is only in the phi direction, in spherical coordinates, the general wave equation simplifies to the polar wave equation for the phi component. The polar wave equation admits the an analytical solution (ref. Clayton R. Paul, Keith W. Whites and Syed A. Nasar, Introduction to Electromagnetic Fields, Mcgraw-Hill College; 3 Sub edition (December 9, 1997), p.590). We call this solution “antenna wave”.

Why EM wave equation does not conform to relativity?
http://pengkuanem.blogspot.com/2012/08/why-em-wave-equation-does-not-conform.html

# Deformation of EM wave signals

Deformation of EM wave signals
14 August 2012

Electromagnetic wave carries signals emitted by antenna into space. The EM field of a wave is mathematically defined by the EM wave equation whose monochromatic solution is the equation (1). A signal is a time varying EM field that can be expressed by Fourier series which is the sum of monochromatic wave functions, that is, a sum of equation (1) of different amplitudes and wave lengths.

We notice that the amplitude and phase of the equation (1) vary with distance and frequency, that is, monochromatic EM waves of different frequencies evolve differently in space. In consequence, the form of the Fourier series is distorted, the traveling signal is deformed. What is the extent of the deformation of EM signal in space?