What is the maximum and minimum of antenna gap of dipole antenna?

Question

Consider the picture below is a design of half wave length ($\lambda$) dipole antenna. I read some explanations saying that it is the best design to get the optimum transmit power. Or it is cut to $0.47 \lambda$ to $0.48 \lambda$ to get the optimum impedance (CMIIW).

But my concern here is, what is the minimum or maximum distance of the gap as in the picture? Gap between the two elements which the feeder line is connected? I expect that the explanation is in $\lambda$. But if you really need the used frequency, that just put 2,100 MHz.

Answer 1

from the standpoint of mathematically modeling the behavior of the split dipole, the gap you describe is taken to be zero or nearly so.

In the real world, a zero gap is impossible and a nonvanishing gap has the effect of altering the feed point impedance of the dipole from its ideal (theoretical) value, thereby upsetting the transmission of power from the transmission line across that termination and into the branches of the dipole.

The mathematics of that effect can be gotten from the helpful experts on the Amateur Radio Stack Exchange and I recommend that you post your question there.