Magnetic force between two long conductive wires with current I was asked to calculate the total magnetic force between two long conductive wires with current on them, flowing in the same direction. I used the formula F$_1$=$μ_o\frac {I_1I_2l}{2πd}$ and got a numerical answer. I then doubled that answer to account for both forces (from either wire to the other). The answer key gives the same number I found, but without doubling it. I do not understand why, because it clearly states in the book that said formula is for the force experienced by wire 1, caused by wire 2, which disregards the force experienced by wire 2, caused by wire 1.
Can anybody help?
 A: You are correct that the force per unit length is $\frac{\mu_0 I_1 I_2}{2 \pi r}$. This is really a consequence of Newton's Third Law. The two forces that you seem to be describing are the same force, which arises from the interaction between the wires. The wires exert a force on each other, and are themselves pulled towards each other as a result. Both wires experience this equal force towards each other.
The same reasoning applies when a stretched spring exerts a force $kx$ on both ends and not $\frac{kx}{2}$. The two forces are a reaction pair. The same goes for electrostatic and gravitational attraction.
A: You should not double it as if the 2nd wire is not there than on what does the 1st wire apply force on.
Lets understand by a simple eg. Say 2 persons are holding a rope (massless) each applying 100N force on it by this statement it seems that tension in the rope should be 200N but its 100N I would explain you that we know that the rope is at rest so we may consider it as one is pulling the rope with 100N attached to a wall (as in both case both persons , wall , as well as rope is at rest ) so now you shall say that tension is 100N.
Same is your case 
