Three long parallel wires lie in the x-y plane (parallel to the y axis). The dis

Question

Three long parallel wires lie in the x-y plane (parallel to the y axis). The distance from the middle wire to each of the outer ones is a = 3.5 mm. The current in the two outer wires is I1 = 4.5 A and is directed in the positive y direction, the current in the middle wire is I2 = 2I1 = 9.0 A and is in the negative y direction. Find the magnitude of the resultant magnetic force acting on unit length of each wire. Force on the left wire = ??? N/m Force on the central wire = ??? N/m Force on the right wire = ??? N/m I know how to find this when it's for two parallel wires, but unsure how to for three. PLEASE help me! If you could show work/ formulas that would be awesome!

Explanation / Answer

Force on middle wire = 0 as the forces from the side wires cancel each other
And by symmetry, the magnitude of force on the side wires is same,
Force per unit length =0I1I2/2d =2 x 10- 7 *(4.5*9/3.5*10-3-4.5*4.5/3.5*10-3)=1.16*10-3 N/m Towrds the middle wire

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