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lets say I have two wires. each has a magnetic field due to its current. this magnetic field is present in the other wire causing a force in that other wire. Now I understand that changing the current of one of the wires doesn't change the fact that the 2 forces are equal and opposite but what about L the length of the wires? what happens if I increase the length of wire A and keep the length of wire B the same as before? doesn't that mean that the force on A is now greater? and if it is greater does that mean newtons 3rd law doesn't apply?

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one theory I had is that the length that is contained within the magnetic field wire B would mean that the force is the same because the length that has a force on it would be the same as B. is this correct?

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  • $\begingroup$ @ThePhoton yes your correct I didn't realize $\endgroup$
    – Safa yousif
    Commented Apr 7 at 8:06

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what about L the length of the wires? what happens if I increase the length of wire A and keep the length of wire B the same as before? doesn't that mean that the force on A is now greater?

Yes, the force on the wire is found by integrating ${\bf J}\times{\bf B}$ over the volume of the wire, and increasing the length of the wire increases its volume, so the force on the wire is greater.

and if it is greater does that mean newtons 3rd law doesn't apply?

No, the force on wire B also increases, because increasing the length of wire A increases the B field in the vicinity of wire B.

Note: If wire A is already much longer than wire B, both effects will be very small. Only if wire A is smaller or similar in size to B will there be a strong increase in the forces from increasing the length of A.

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  • $\begingroup$ so increasing L has an effect in the magnetic field made by A? I didn't know that thank you. $\endgroup$
    – Safa yousif
    Commented Apr 7 at 8:03
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In the static case Newton's third law applies and whatever change in the forces acting on wire $A$ due to wire $B$ is experienced by the forces on wire $B$ due to wire $A$.

Please also note that in general you cannot have a wire carrying a current without there being a complete circuit. In your diagrams there are missing wires connected to a voltage source carrying a current. Thus, unless you are dealing with wires that are "infinitely" long, you are always making an approximation regarding the magnetic fields produced by the wires.

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  • $\begingroup$ the diagrams were just to convey what my question was but yes they are supposed to be connected. $\endgroup$
    – Safa yousif
    Commented Apr 7 at 8:04

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