# Electric Field in Circular waveguide in TE mode

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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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 $E_z=0$.