On Wikipedia it says:
This force is used in the formal definition of the ampere, which states that it is "the constant current that will produce an attractive force of $2 × 10^{-7}$ newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum."
In reference to the definition of an Ampere, why was $2 × 10^{–7}$ chosen?
Answer
The definition of Ampere is obtained by the below equation of force between two infinitely long parallel current carrying conductors.
Where $F$ is force, $\triangle{L}$ is small length element, $\mu_0$ is absolute permeability of vaccum or free space, $I_1, I_2$ are current flowing through two conductors.
By calculation we can obtain that $\frac{\mu_0}{4\pi}=10^{-7} T A^{-1} m$
When $\triangle{L}=1m, I_1=I_2=1A, r=1m$. By substituting the values in the above equation given in the figure, we obtain $\frac{F}{\triangle{L}}$ to be equal to $2X10 ^{-7}N m{-1}$.
Thus we have the definition of one ampere as: One ampere is that current, which when flowing through each of the two parallel conductors of infinite length and placed in free space of one metre from each other, produces between them a force of $2X10^{-7}$ newton per metre of their lengths.
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