Two parallel long $($infinite for our purposes$)$ wires are suspended by a system of thin strings of length L$=2\mathrm{.}1$cm each as illustrated in the figure below showing the plane perpendicular to the wires. These wires

are part of the electric circuit and run the same $($but unknown$)$ current I in the opposite directions. We treat the current II and $-$I next to the wires' position in the figureB as shown with the magnitude B$=2\mathrm{.}8$G$.$ As appropriate for the wires,

their "weight" is quantified by the linear mass density, it is equal to $16\mathrm{.}5($g$)/($m$).$

The wires are found in mechanical equilibrium when each of the strings is at angle $\backslash$theta $=6\mathrm{.}85\backslash$deg from the vertical as shown in the figure. This equilibrium can be realized, however, for both directions of the current in

the wires.

Find current I$=$I$\_(1)$ enabling the equilibrium when it is positive $($I$\_(1)>0)$ :

I$\_(1)=2\backslash$times $,$A$.$

Find current I$=$I$\_(2)$I$\_(2)<mn>0</mn>$ I$\_(2)=2\backslash$times $,-18\mathrm{.}8$A$.$