# A Jackson E&M: Power loss in waveguides for TE & TM modes

#### IcedCoffee

Hi. I'm having trouble with calculating

(8.59)

from (8.58)
($\vec H_{//}$ is simply $\vec H$ in Jackson, but that shouldn't matter.)

in Jackson. Specifically I think I'm not sure about parallel component of H field here.

For example, shouldn't I have two terms for the TE case in that

when $\hat n = \hat x$ (for simplicity), $\hat n \times \vec B = - B_z \hat y + B_y \hat z = B_z \hat y + \frac {ik} {\mu \epsilon \omega^2 - k^2} \frac { \partial B_z } {\partial y} \hat z$ (from 8.26b)

(which, by the way, does not include $\frac {\partial B_z} {\partial x}$ as in Jackson)

And similarly, shouldn't TM mode have only one term since $B_z$ is zero in TM mode?

Related Classical Physics News on Phys.org

"Jackson E&M: Power loss in waveguides for TE & TM modes"

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