# Three current-carrying wires

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 $$+y$$ direction through the wires M and N are $$2I$$ and $$I$$, respectively. The magnetic field strength at all points of the $$y$$-axis induced by these three currents is zero. Then what are the direction and intensity of the current flowing through the wire L?

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