Electric field due to an uniformly charged ring: problem to plot a specific graphic

Question

We know that the intensity of an electric field $E_x$ due to an uniformly charged ring ($R$ is the radius, $r=d(\text{charge $dq$},P)$)

is $$E_x=\frac{k_e\ q\ |x|}{(x^2+R^2)^{3/2}}\tag 1$$

where $k_e\approx 9\cdot 10^9$ N$\cdot$ m$^2$/C$^2$, and $q$ is the charge of the ring.

Since $k_e$ is very big, how appropriately should I choose $q$ (the charge) and $R$ (radius of the ring) to obtain the image below?

Addendum: Here there is an image of the function $(1)$ with $q=R=1$:

Without $|x|$:

Answer 1

The main factor here is the large factor you are multiplying the function by. When plotting, it can be useful to play with parameters to get a good idea of what the curve looks like. If parameters are too large, the general shape of the curve can be hidden by the sheer size of the values. I believe that is what is happening with your graph here. The graph is odd because the scaling factor is very large, but if you zoom out, you should see the curve you want.

From Andrei's comment,

I would choose $q=\frac1{9\cdot10^9}$. That's the equivalent of plotting $\frac{E}{kq}$.

Plot for $f(x)=\frac{|x|}{(x^2+1)^{3/2}}$:

Plot for $f(x)=100\frac{|x|}{(x^2+1)^{3/2}}$: