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I know that the magnetic field inside a circular waveguide is

$B_z=B_0\dfrac{\rho}{R}\left(1-\dfrac{\rho}{2R}\right)\cos{\phi}\sin{\frac{\pi z}{d}}$

How can I find the two components of the electric field, $E_\rho, E_\phi$ that is?

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I have some doubts about your formula. It is my understanding that radial dependence of fields in circular waveguides is described by Bessel functions (see, e.g., )

EDIT (04/21/2013) I've just had a chance to look at Jackson, Classical Electrodynamics, 3rd ed. (please see @Thanos' comment below) The formula in your question is indeed approximate - it is used as a trial function in the variational principle. To find the components of electric field, you need to use Jackson's formula 8.26a, assuming $E_z=0$.

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Thank yo very much for your answer! Actualy, this is exactly the field inside the circular waveguide(see Jackson, 3rd edition, Pr. 8.10) and I had the same doubt as you! – Thanos Apr 18 '13 at 11:21
Well, I don't have Jackson's 3rd edition, so I have nothing to say so far... – akhmeteli Apr 18 '13 at 12:12
Thank you very much for your time, anyway! – Thanos Apr 18 '13 at 12:18

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