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Where does the energy go when two EM waves interfere?

 


In radio engineering it's well known that interference reduces the strength of the signal. 


With respect to interference we talk about things like constructive and destructive interference. In constructive interference signals are in phase and reinforce each other. 


In destructive interference signals are out of phase and cancel each other. 

But when we talk in terms of energy, when we consider electromagnetic waves as propagating energy sources a different question arises

How does interference affect the energy of the wave,if it does at all? 


Now it's quite obvious that unlike signals that can lose information energy can't be "lost". However energy can be transformed as well as transferred.  In that case does the transfer of energy happens within the wave or between the interfering waves. 


Or to put it another way does the wave that carries energy lose it to another in case of destructive interference and gain it from another in case of constructive interference?


This understanding is of great importance in wireless energy transmission systems. 


An electromagnetic wave consists of electric and magnetic components. The transformation of energy happens within these components  


As shown in this paper by Kirk T MacDonald of Princeton University


http://www.physics.princeton.edu/~mcdonald/examples/destructive.pdf


A destructive interference in EM waves doubles the electric energy but destroys the magnetic energy of the wave. 


A constructive interference doubles the magnetic energy but destroys the electric energy of the wave. 


In both cases the total energy of the wave remains constant or conserved.  

Effect of transformation on signal 

We know that information is encoded in the electric field by a modulating current at the transmitter. At the receivers end this electric field produces a current that is demodulated. 


Now if we apply these observations to signal theory in radio engineering we find that  since in destructive interference the electric component is modified so is the information. 


But the loss of Information does not mean loss of energy. As noted, the wave energy is conserved in magnetic/electric fields. 

The electrical nature of the EM wave 

In EM waves there is no electric charge. Just like you can't get shocked by sunlight you also can't get shocked by a radio wave. 

But just as you can get burned by intense sunlight you can also get burned by radio waves,if the intensity is high enough. 


https://physics.stackexchange.com/a/19633


A question arises then ,if there is no electricity in EM waves then what is the E component in EM.


Relationship between electric field and electric charge


That E in EM refers to an electric field. We know that a static Electric field is a force. A moving electric field,such as the one in a propagating wave is energy. 


More explanation...


It is common knowledge that electric charges create fields. Static charges create static field and moving charges create moving field. This is a well understood principle. 


But electric charges are not the only things that create and electric field. A changing magnetic field can also create an electric field. This electric field will affect electric charge but they are not composed of it. 


In other words the electric field is not the cause of the electric charge but the effect.


 An electric charge has an electric field. A moving magnetic field also has an electric field but without electric charge. 


This is the fundamental principle of EM wave propagation where electric and magnetic fields feed off each other. 


EM waves are pure energy that can be converted into other forms of energy like heat,or wind or electricity. We're already familiar with the conversion process as in converting sunlight to electricity, or sunlight to heat etc.  


Since energy cannot be destroyed all interference does is change one form of EM energy into another. 

From the point of view of wireless transmission of energy the presence of other EM waves will not destroy the energy of the transmitting wave. 



About superposition that still applies but since in EM waves the direction of propagation is a cross product of E and M it is possible for interfering waves to combine their Es and conserve energy. Or Ms for that matter depending upon the direction


Here's the answer by Prof Hanz that explains it well with diagrams as well as with a link to his paper. It's a good read and I encourage you to check it out.


https://www.quora.com/When-2-waves-interfere-destructively-what-happens-to-the-energy-of-the-waves/answer/Hans-Schantz?ch=10&share=b1d03315&srid=LNunv


There's a lot we can learn from EM waves that can help us in the future for energy conservation, generation as well as transmission. This is an area of research that should be picked by universities.


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