$9.2.4.$ A force of $2.5\cdot 10^{-7}$ N acts on a unit of length of a straight long wire with current from the side of a second wire with the same current. The distance between the wires is $1$ m, the current in the wires is 1 A. What is the magnetic permeability of this medium?
Magnetic induction of one wire with current $I$ $$ B = \frac{\mu_0 \mu I}{2\pi R} $$ The force acting from the magnetic field $B$ on a piece of wire $\Delta l$ with a current of $I$ $$ F = BI\Delta l = \frac{\mu_0 \mu I^2 \Delta l }{2\pi R} $$ Where do we express the magnetic permeability of the medium? $$ \boxed{\mu = \frac{2\pi F R}{\mu_0 I^2 \Delta l } = 1.25} $$
$$\mu = 1.25$$