Force between two parallel wires carrying current?

[21joanna12]

There is something I am confused about when it comes to the force between two parallel wires carrying current, specifically why when they carry current in the same direction the wires are attracted to each other. I understand that when you use Flemming's left hand rule and consider the electrons in each wire moving in the other wire's magnetic field separately, then you see that the force on the electrons in each wire is towards the other wire. Also, when you consider relativistic effects, the electrons in each wire see the electrons in the other wire being stationary relative to them, but they see the positive ions moving backwards. This means that they would see the space between the ions to be contracted, so the positive ion density is greater and the wire has an overall positive charge, and so the negative electrons are attracted to the other wire. However when I think about the interaction of the fields created by each wire, I think that wires carrying current in the same direction should be repelled. Field lines cannot cross each other or go in more than on direction at a point. From what I understand, this is one way that you can think of like poles of a magneti repelling each other- the field lines coming from each pole cannot cross. When I think of wires carrying current in the same direction, the magnetic fields between the wires will be going in opposite directions and will be opposing each other. The field lines can't be in the same place and pointing in opposite directions, and so the wires will be repelled. Also, when the wires carry current in opposite directions, the field lines between the wires point in the same direction and can merge, like the field lines from a north and South pole of a magnet merge, so the wires should be attracted. I'm not quite sure what is wrong with my thinking here...

I apologise if I have put this in the wrong forum- I wasn't sure if to put it in general physics instead...

Thank you in advance!

EDIT: I just realized that I also have a question about explaining the force between the wires when the current in one wire is more than twice the current in the other wire. If this were the case, then then considering the electrons in the wire with a smaller current, it would see the electrons in the other wire as having a greater speed relative to it than the positive ions so, so theoretically the electrons should now see that the other wire has a greater negative charge desnsity than positive charge density, and the wire should be repelled even thought thecrens flow in the same direction. On the other hand, in the wire with the greater current the electrons would see the positive ions in the other wire as having a greater negative velocity than the electrons, so the wire with the larger current would see the wire with the smaller current as having an overall positive charge density, and therefore would be attracted to that wire. This makes no sense because if one wire both wires should either be attracted to each other or repelled from each other by Newton's third law...

I apologise that this is turning out to be such a long post! Thank you in advance for reading it!

 

[harrylin]

There is something I am confused about when it comes to the force between two parallel wires carrying current, specifically why when they carry current in the same direction the wires are attracted to each other. I understand that when you use Flemming's left hand rule and consider the electrons in each wire moving in the other wire's magnetic field separately, then you see that the force on the electrons in each wire is towards the other wire. [..]

However when I think about the interaction of the fields created by each wire, I think that wires carrying current in the same direction should be repelled. Field lines cannot cross each other or go in more than on direction at a point. From what I understand, this is one way that you can think of like poles of a magneti repelling each other- the field lines coming from each pole cannot cross. When I think of wires carrying current in the same direction, the magnetic fields between the wires will be going in opposite directions and will be opposing each other. The field lines can't be in the same place and pointing in opposite directions, and so the wires will be repelled. Also, when the wires carry current in opposite directions, the field lines between the wires point in the same direction and can merge, like the field lines from a north and South pole of a magnet merge, so the wires should be attracted. I'm not quite sure what is wrong with my thinking here...[..]

Hi Joanna, to help with disentangling some issues I left out the SR considerations in order to focus on the classical questions.
Fields act on matter - your consideration of how magnetic fields act on moving charges is correct.

In contrast, your consideration of how field strengths add up in the space between the wires does not tell you anything about the forces on the wires. I'm therefore a bit suspicious about the field line explanation of repelling magnets that you presented (is that understanding based on a textbook? If so, which one?).
And for currents in opposite directions, it goes the same. Merged field lines in empty space don't act on anything; what matters is the interactions of the fields with the wires. Just my 2 cts. :)

 

[21joanna12]

Hi Joanna, to help with disentangling some issues I left out the SR considerations in order to focus on the classical questions.
Fields act on matter - your consideration of how magnetic fields act on moving charges is correct.

In contrast, your consideration of how field strengths add up in the space between the wires does not tell you anything about the forces on the wires. I'm therefore a bit suspicious about the field line explanation of repelling magnets that you presented (is that understanding based on a textbook? If so, which one?).
And for currents in opposite directions, it goes the same. Merged field lines in empty space don't act on anything; what matters is the interactions of the fields with the wires. Just my 2 cts. :)

Thank you for your reply! The field line explanation mostly comes from my teacher, but something similar is said here at 1:45 although it is not stated as explicitly as my teacher stated it... Although thinking about it now I realize that it is not like the field lines from each magnet are fixed and so cannot be on top of each other, it is more like the field lines will add and will create a new field with just one set of field lines, so there is no crossing! Although my teacher used a similar explanation for why two like charges repel each other, but using electric rather than magnetic fields. In the case of like charges, should you also only consider each of the charges in the other charge's field separately, or should you consider the superposition of the fields? Thank you!