# Three current-carrying wires 2

As shown above, three infinitely long current-carrying wires L, M and N are fixed on the $$xy$$-plane, all parallel to the $$y$$-axis. The distances from the $$y$$-axis are $$2r$$, $$r$$ and $$r$$, respectively. The intensities of the currents flowing in the wires L, M and N are $$2I$$, $$2I$$ and $$I$$, respectively. The direction of the electric current in L is $$-y$$ direction and the directions of the electric currents in M and N are both $$+y$$ direction. Let $$F_L, F_M$$ and $$F_N$$ denote the sum of the magnetic forces acting on each of the segments (of the same length) of $$L,$$ $$M$$ and $$N,$$ respectively. Then what is the ratio $$\lvert{F_L}\rvert:\lvert{F_M}\rvert:\lvert{F_N}\rvert?$$

×