Electronic – Does the letter k in electromagnetics represent wavenumber inside a cosine

electromagneticelectromagnetism

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

Best Answer

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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