Magnetic constant in vacuum: different values in the Italian textbooks for high school My simple question is that in different Italian textbooks I have seen that the magnetic constant in vacuum $k_m$ is defined as:
$$k_m=\frac{\mu_0}{2\pi} \tag 1$$
Below there is a screenshot of my digital book written also with MathJaX where there is the name of the book.

After from the book, Walker in Italian language:


While in my university notes I have 
$$k_m=\frac{\mu_0}{4\pi} \tag 2$$ 
Surely the correct value is the $(2)$. Any observation or comment is welcome.
 A: Modern usage is that “magnetic constant” means $\mu_0$ (with no $2\pi$ or $4\pi$) and “electric constant” means $\epsilon_0$ (with no $4\pi$).
It is common to call $k_e=1/4\pi\epsilon_0$ the Coulomb constant. Wikipedia defines $k_A=\mu_0/4\pi$ but does not call it the Ampere constant, although the notation suggests this.
I have never seen anyone give $\mu_0/2\pi$ a symbol such as $k_m$, and doing so strikes me as bizarre given that $\epsilon_0\mu_0=k_A/k_e=1/c^2$. Using $k_m=\mu_0/2\pi$ instead of $k_A=\mu_0/4\pi$ would get rid of the 2 in Ampere’s force law, but at the cost of introducing a factor of 2 into the more fundamental relation between electricity and magnetism in the previous sentence.
The theorists I have worked with have always used Gaussian units (and also $c=1$) where there are none of these constants to worry about! As far as I am concerned, SI units are for experimentalists and engineers and do nothing but obscure electromagnetism. This is especially the case when teachers still use obsolete terms like “vacuum permittivity” for $\epsilon_0$ and “vacuum permeability” for $\mu_0$, which suggest — wrongly — that there is something physical about these constants.
