If b a ,Ex and Hy are zero .why ?

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In electromagnetic field theory, when the parameter b is significantly greater than a (b >> a), the electric field components Ex and Hy become zero, leaving only Ey, Hx, and Hz present. This phenomenon is explained through boundary conditions in waveguide theory, particularly in rectangular waveguides. The Fourier solution to the 2D wave equation indicates that Ex and Hy are proportional to sin(1/b), which approaches zero as b increases. The discussion also highlights that specific boundary conditions, such as those involving perfect magnetic conductors, can result in certain field components being zero. Understanding these relationships is crucial for solving related exercise problems in electromagnetic theory.
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if b >> a ,Ex and Hy are zero .why ?

hello friends...in schaum series book on Electromagnetic field theory , its shown that if b>> a then Ex and Hy are zero , and only components present will be Ey , Hx, Hz...
can you please tell me the reson for that...what happened when we made b >> a...
( i know that if a > b the all five components mentioned above r present...)

i have uploaded image of rectangular waveguide...
 

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It is just the way it is.
 


Do you really mean b >> a and not like in your picture a>b like for a usual rectangular waveguide? If you really mean b>>a, you might find the solutions with a parallel plate waveguide. Furthermore since I am curious, could you supply a amazon.com link to the book you use?
 
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I believe that in the Fourier solution to the 2D wave equation with the rectangular waveguide boundary conditions, Ex and Hy are proportional to sin(1/b), and if b is very large then this would make the components go to zero. I'm not sure if that's what the problem is stating though.
 
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Hmm, I thought in rectangular waveguide problems, depending on type of boundary conditions used, the relevant tangential components to sides are 0. That might be why. For example, if a perfect magnetic conductor(pmc) boundary was employed at the left wall of the waveguide above, then Hy component at that wall would be 0 due to pmc condition and so on. Similar situation with the pec condition.
 

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