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I am having a intellectual debate with a colleague on whether k (in this equation below) represents the wavenumber k (that is used in electromagnetics) or does k in this question not refer to wavenumber k and is k just some letter? My understanding of this question is that t is time, z is space, and k is wavenumber.

The question states: The magnetic field of a wave in free space and in cylindrical coordinates is given by enter image description here where t is in seconds, and r and z are in meters. (a) Determine k. (b) Assume k = 1 (rad/m). Consider a square contour C in the y = 0 plane as shown in the following figure. Find the line integral of the electric field along C in the direction shown enter image description here

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Yes, it does. The unit for wavenumber k is radians/m (2*pi/lambda) and unit for z(coordinate) is meters. When you multiply both, you end up with radians inside a cosine. Which is perfectly logical.

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  • \$\begingroup\$ I want to make sure I understand. You are saying that it's clear from the question that k is implied to be the wavenumber? Thank you for your time :) \$\endgroup\$ Jun 2, 2020 at 14:56
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    \$\begingroup\$ @user5574422 it is kind of always like that, i.pinimg.com/originals/ba/af/cf/… \$\endgroup\$
    – muyustan
    Jun 2, 2020 at 14:58
  • \$\begingroup\$ I’ve also seen wavenumber’s nomenclature also be the Greek letter “nu” which is \$\nu\$, kind of looks like a Latin “v”. \$\endgroup\$
    – user103380
    Jun 2, 2020 at 15:04
  • \$\begingroup\$ @KingDuken I have seen "nu" as frequency during most of my learning, so it automatically represents frequency to me. But don't know if it is common among the entire community or not. \$\endgroup\$
    – muyustan
    Jun 2, 2020 at 15:11
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    \$\begingroup\$ Apologies, I was just simply stating that I've also seen "nu" as linear wavenumber (see under "Definition"), I wasn't trying to say/imply that you were wrong with your answer. I think I got my definitions mixed up with linear wavenumber and angular wavenumber. \$\endgroup\$
    – user103380
    Jun 2, 2020 at 15:37

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