Microwave rectangular cavity resonator ?

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Dhruv
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Homework Statement


I am putting the picture of the equation given to me in book , I feel it to be wrong please tell me that is the equation written in book correct or not !

Homework Equations

The Attempt at a Solution

 
Attachments
  • Handwritten derivation on lined paper: 'According to me', cos βd = 0, so βd = (2n+1)π/2, then β = (2n+1)π/2d, boxed as the final result.
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  • Printed textbook page with derivation of TM and TE mode field equations in a rectangular waveguide, including E_z = C sin(mπx/a) sin(nπy/b) cos(pπz/d) and a labelled box diagram of the guide with dimensions a, b and d.
    image.jpg
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mfb said:
I agree with your result.
Thnx :) this really helped.
 
Dhruv said:

Homework Statement


I am putting the picture of the equation given to me in book , I feel it to be wrong please tell me that is the equation written in book correct or not !

Homework Equations

The Attempt at a Solution

Can 't make out the text image (cut off on the right) so couldn't comment.
 
rude man said:
Can 't make out the text image (cut off on the right) so couldn't comment.
Sorry for inconvenience.
 
Attachments
  • Handwritten derivation on a textbook page (page 177) covering TM and TE waves in a rectangular waveguide, with equations 5.25 and 5.26 and a labelled waveguide diagram (Fig. 5.6) showing axes x, y, z and dimensions a, b, d.
    image.jpg
    68.2 KB · Views: 441