Question

Today we learned about the Hertzian Dipole. Out teacher told us that the length of the wire connecting the two capacitor plates is l=λ2. He also stated that there is a no more phase shift (I don't know the correct English word) in the far field, which starts also at λ2. Unfortunately he could not explain why the phase shift disappears in the far field and why it is at λ2

. I have read up on the internet and in textbooks, but only found the fact that this is the case, but not why? Are Maxwell's equations necessary to explain this? How can this be explained mathematically or physically?

Answer 1

In the far field of the Hertzian dipole, the phase shift disappears and the wavelength is equal to half the length of the wire connecting the two capacitor plates (λ/2). This can be explained mathematically and physically using Maxwell's equations.

Step-by-step explanation:

In the far field of the Hertzian dipole, the phase shift disappears and the wavelength is equal to half the length of the wire connecting the two capacitor plates (λ/2). This can be explained mathematically and physically using Maxwell's equations.

In the far field, the electric field produced by the dipole can be approximated as a plane wave. The phase of a wave is determined by the distance it has traveled, and in the far field, the phase shift disappears because all points on the wavefront have traveled the same distance.

Additionally, the wavelength in the far field is equal to half the length of the wire connecting the capacitor plates. This is because the wire acts as a half-wave dipole antenna, where the wire length is resonant with the wavelength of the radiation it emits.