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What is the direction is the magnetic force vectors pointing from a coil of wire that has current running through it?

The above link is a picture of a wire with current running through it. I see the blue arrows indicating the magnetic field lines, but I am having trouble visualizing the magnetic force lines. Where are they pointing? Please help.

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There are no such things as magnetic force lines. The magnetic force is given by the Lorentz force law. – Mark Eichenlaub Mar 27 '11 at 6:56
Don't be silly, Mark. Magnetic field lines - at least in this form - is a totally standard term, see e.g. - and while charged bodies are affected by the Lorentz force, the force acting on a magnetic dipole try to rotate them in the direction of the field lines. – Luboš Motl Mar 27 '11 at 7:02
@Lubos Yes, I agree explaining what field lines are might be helpful. But the OP says "I see the field lines, but I want to know where the force lines are." So if you already have the field lines down and are looking for some other sort of lines, it seems like you're barking up the wrong tree. That was my point. – Mark Eichenlaub Mar 27 '11 at 7:07
I see - but I don't think it was QEntanglement's worry (how to tautologically rephrase "field lines" as less accurate synonym "force lines"). Instead, I think that the question was asked because its author couldn't decode the 3D arrangement out of the confusing 2D projection. So he asked about the signs of the magnetic fields, didn't he? – Luboš Motl Mar 27 '11 at 7:12
Dear Mark, apologies - I just want to say that you were completely right. OP was barking on the wrong tree and exactly meant how you understood it. – Luboš Motl Mar 27 '11 at 7:49
up vote 2 down vote accepted

Let me start from your comment on Lubos' answer:

If we have a electron near a coil of wire that has current running through it, certainly the electron will move a certain direction right?

No, it's not that simple. For a given coil of wire producing a given magnetic field, the electron can experience a force in any direction that is perpendicular to the field. It depends on which way the electron is moving. (The force is always perpendicular to both the field and the electron's velocity.) In fact, if the electron is just sitting at rest, or is moving parallel to the magnetic field, it experiences no force at all.

You might be confused because you're thinking of the electrostatic force. That one is always parallel to the electric field; it doesn't matter how the particle is moving, and that's why you can draw electrostatic force lines. But that doesn't work with the magnetic force.

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What is the question you are answering @Dave? – user346 Mar 27 '11 at 8:36
@Deepak: the one that QEntanglement originally asked. More precisely, I'm explaining why the second part of that question doesn't have any meaningful answer. (Unrelated: I would be interested to know why I was downvoted) – David Z Mar 28 '11 at 1:02
That wasn't me @David. I ask questions first and down-vote (or upvote) later. Unless the answer is manifestly BS. – user346 Mar 28 '11 at 11:57
@Deepak: Yeah, I didn't think it was you. (That's why I said "unrelated" although in retrospect I see why that wasn't clear) – David Z Apr 2 '11 at 4:13

the magnetic field is given by Ampere's law and the direction is determined by the right-hand rule:

enter image description here

If the current goes in the direction of the right thumb (convention for the direction of current is from plus to minus), the remaining fingers show the direction of $B$ around the wire.

See also

For a bar magnet, the magnetic moment is directed from South to North; it's also the direction in which the magnet will try to rotate in an external $B$ field of the same direction. See e.g.

Of course, those rules - and why direction is chosen rather than the opposite one - depend on a couple of conventions that physicists ultimately adopted globally. Some of the "signs" in the conventions are independent, others are not.

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In your picture, with the green wire, I see the magnetic field and the current, but where is the force pointing? And now what I am confused about is if you now coil this wire up in the picture I have attached, where are the force lines pointing? – QEntanglement Mar 27 '11 at 7:33
Which force? There is more than one force on the Universe. Different objects with different charges and magnetic moments etc. will see different forces - including different signs - acting on them. Mark was apparently right. You're just totally confused about the meaning of the word force, among other things. There is nothing such as a "universal force" caused by a wire. – Luboš Motl Mar 27 '11 at 7:46
If we have a electron near a coil of wire that has current running through it, certainly the electron will move a certain direction right? and a positron will move the opposite direction. This must be due to the magnetic force right? Depending upon where you put the electron near a coil of wire, it will move differently. SO, the force lines must point out in some configuration out of the coil of wire that has current running through it. THIS is what I'm trying to ask, how does the picture look adding force lines to the drawing? – QEntanglement Mar 27 '11 at 7:51

The tangent to any magnetic field lines at a point gives the direction of the force at that point on an imaginary isolated north pole whose own magnetic field strength is negligible to change the original field. the direction of magnetic lines of force for a current carrying conductor can be known by an easy method. just imagine to grab a current carrying conductor with your right hand with the thumb pointing towards the direction of the flow of current. The alignment of the other fingers will point to the direction of the magnetic lines of force.

enter image description here

In case if you would like to know the law which is called the Biot-savart law is given by enter image description here enter image description here

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