t - Time elapsed
n - Number of charges oscillating
d - Distance between consecutive charges (in multiples of λ)
t - Time elapsed
n - Number of charges oscillating
d - Distance between consecutive charges (in multiples of λ)
The patterns in the electric field vectors are from a phenomenon called undersampling. The field is still physically correct; it's just that visually it looks somewhat odd.
Imagine a sine wave. If we want to approximate its shape, we can sample points on it and then connect those points.
Now, if we put a point on every peak and valley of that sine wave, we get a very crude approximation, but one that still has a wavy shape.
If we sample points closer to one another, the approximation gets better and better.
But if we sample points less frequently than at every peak and valley, we lose information, because we do not know where the valleys and peaks are anymore.
This is what happens in the electric field representation above. Because of graphical limitations, the space between the vectors is larger
than half a wavelength of the electromagnetic waves, and so some information is lost.
(This explanation is not exactly correct, see more about the Nyquist–Shannon sampling theorem)
If you are curious about the math, here is some:
From the charges to the end of the electric field visualization, there is $1000 \text{ m}$ horizontally. There are $50$ vectors; that means a vector every
$\frac{1000}{50} = 20 \text{ m}$. For the "minimum sampling requirement" above to be satisfied, then, we would have to have $\lambda \gt 40$.
But there is another catch. For the far field approximation of the intensity pattern to be correct,
the distance we observe must be way greater than $D$, where $D$ is the distance from the top charge to the bottom one.
Let's take the maximum possible $D$, that is $D_{max} = (n_{max} - 1) d_{max} = 4 \cdot 3 \lambda = 12 \lambda$.
Let's say that a "great distance" means at least $10D = 120 \lambda$. We still have $1000 \text{ m}$ to use, so $\lambda \lt 8.33 \text{ m}$.
These two conditions contradict one another, so it is not really feasible to create a visualization where the far field approximation is correct and
the waves are still nicely visible.
Please disregard those odd patterns in the electric field representation detailed above! It is still nicely visible where the intensity is greatest and where it is near zero. Try changing $d$ and $n$. Notice that changing $n$ does not affect the spacing of the maximum intensity points (this is best viewed at $d = 3$). Also, changing $d$ does not affect the intensity of the peaks (this is best viewed at $n = 5$).
The opacity of the electric field vectors is dynamically scaled based on their magnitude. This is a visual effect used to make the propagating waves clearly visible across the canvas.