Why do Parallel Currents Attract?

[what_are_electrons]

I've read that when currents in two parallel wires are going in the same direction, they attract each other. The same text said that when the currents are going in opposite directions, the two wires repel each other.
Why does this happen? Is there a different behavior for AC and DC currents?

 

[daveed]

its because of the right hand rule, which describes how magnetic fields/the magnetic force work

 

[what_are_electrons]

its because of the right hand rule, which describes how magnetic fields/the magnetic force work

Please explain with a bit more detail. Thanks!

 

[kuenmao]

let's say that there are two wires, with their current mving towards us from a far place. The wire on the left generates an upward magnetic field at where the wire on the right is. Using Fleming's left hand rule, we find that the electromagnetic force acting on the wire on the right is directed towards left. Vice versa applies, and the wire on the left is pushed towards the right by another electromagnetic force. This makes it look like an attraction.
When the currents move in opposite directions, the eletromagnetic force causes them to repel each other in a similar way. You can work it out yourself :)

 

[what_are_electrons]

let's say that there are two wires, with their current mving towards us from a far place. The wire on the left generates an upward magnetic field at where the wire on the right is. Using Fleming's left hand rule, we find that the electromagnetic force acting on the wire on the right is directed towards left. Vice versa applies, and the wire on the left is pushed towards the right by another electromagnetic force. This makes it look like an attraction.
When the currents move in opposite directions, the eletromagnetic force causes them to repel each other in a similar way. You can work it out yourself :)

If the two wires are side-by-side wouldn't the magnetic force of both wires point upward toward the ceiling?

 

[Galileo]

If the two wires are side-by-side wouldn't the magnetic force of both wires point upward toward the ceiling?

No, the magnetic field of a wire 'curls around' the wire with the direction given by the righthand rule:
Curl your fingers slightly. If your thumb points in the direction of the current,
your fingers point in the direction of the magnetic field.

The direction of the magnetic force on a charged particle or current is also indicated by
a right-hand rule. If your fingers curl from the direction of the current to the
direction of the magnetic field over the smallest angle, your thumb will point
in the direction of the magnetic force.

So imagine 2 wires drawn vertically on the board with current flowing upwards.
The magnetic field of the right wire points out of the board at the position
of the left wire. Then the magnetic force on the left wire points to the right.
Same kind of argument shows the that force on the right wire points to the left.

In AC currents, the direction of the current changes all the time, but it
still flows in the same direction in both wires at any given time.

Why do Parallel lines merge at the Horizon limit?

This has to do with perspective. Parallel lines seem to merge in the distance, but the distance will remain the same. It has nothing to do with physics.

 

[what_are_electrons]

If the magnetic field is the cause for the attraction, then what property of the magnetic fields actually produces the attraction?

 

[Galileo]

If the magnetic field is the cause for the attraction, then what property of the magnetic fields actually produces the attraction?

A magnetic field exerts a force on a moving charge:
$$F_{mag}=q(\vec v \times \vec B})$$
This is the Lorentz Force Law.

 

[Metallicbeing]

I've read that when currents in two parallel wires are going in the same direction, they attract each other. The same text said that when the currents are going in opposite directions, the two wires repel each other.
Why does this happen? Is there a different behavior for AC and DC currents?

If you have two vertical wires with current moving up them, then the left side of the wire is the north pole and the right side of the wire is the south pole (N / S N / S). Opposite poles attract, right?

Now, let's run the current down the right wire instead of up. The poles on the left wire remain the same while the poles on the right wire have reversed (N / S S / N). Like poles repel.

If you use AC fed into the same end of the wire, they will attract. If you feed AC into opposite ends of the wire, they will repel.

Same End /\/\/\/\ Opposite Ends /\/\/\/\
----------/\/\/\/\---------------\/\/\/\/

(Note: Of course, you need a complete circuit for current to flow)

Try to keep it simple, guys.

 

[Hurkyl]

Another way to look at it is that currents obey an inverse square law, just like masses and charges.

It's just, because currents are vectors instead of scalars, you have to use the dot product instead of ordinary multiplication.

$$\vec{F} = C \frac{\vec{I}_1 \cdot \vec{I}_2}{|\vec{r}|^2} \hat{r}$$

I forget what the constant C should be, but it's negative.


Of course, this is only exact in the static case, or when you can otherwise ignore the propagation delay of the magnetic field.

 

[employee #416]

I think what_are_electrons is wanting to know what distinctive characteristics of magnetic fields gives rise to attraction. What make two fields attract or repel? He is not wanting equations (I'm assuming...), but he is wanting an explanation of how forces are able to attract or repel. The equation just tells whether or not there will be attraction or repelling. If he doesn't want a more descriptive answer, I sure would like to know. So, can anyone answer me this?

 

[pervect]

I think what_are_electrons is wanting to know what distinctive characteristics of magnetic fields gives rise to attraction. What make two fields attract or repel? He is not wanting equations (I'm assuming...), but he is wanting an explanation of how forces are able to attract or repel. The equation just tells whether or not there will be attraction or repelling. If he doesn't want a more descriptive answer, I sure would like to know. So, can anyone answer me this?

There are some interesting remarks one could make about the magnetic field being a sort of relativistic correction to the columb field, but it would be hard to express these comments in very elementary & simple terms that are being asked for.

So the best that can be said in simple terms is that magnetic fields exert a force on moving charges according to Lorent'z force law. I could provide a link to the details of this law, but it seems that that's not really the question being asked - if anyone is interested, I can say more about this law. One also has to realize that a current consists ultimately of moving charges to appreciate this explanation in terms of the Lorentz force law. A current in a wire actually consits of some charges that are moving, and some charges that are not. Fortunately, the non-moving charges don't generate any force by the Lorentz force law.

Perhaps "what_are_electrons" is attempting to ask a philosophical or metaphysical question. In this case, the philosphy forum would be more appropriate. From a scientific point of view, we can explain what things do. One can talk a bit about the history of how things were discovered, i.e. how the magnetic field of a current was discovered when someone noticed a compass needle moving near a wire carrying a current. We can even offer differing models, some of the more elegant models require a bit of sophistication and learning of the simpler models to appreciate. But science can't answer the philosophical questions, which generally have the tendency to go on and on and on, because they basically don't make any difference to results that can be measured.

 

[Metallicbeing]

I kind of remember reading somewhere that a magnetic field occurs due to synchronized electron spin throughout a conductive material. From the spin there are virtual photons emitted and these become force carriers.

Any material with enough electrons with the same spin (or could be made to have the same spin [permeable]) would be attracted. Any material with enough electrons with an opposing spin would be repelled.

I don't know if this is true, but it sure sounds good.

 

[what_are_electrons]

I kind of remember reading somewhere that a magnetic field occurs due to synchronized electron spin throughout a conductive material. From the spin there are virtual photons emitted and these become force carriers.

Any material with enough electrons with the same spin (or could be made to have the same spin [permeable]) would be attracted. Any material with enough electrons with an opposing spin would be repelled.

I don't know if this is true, but it sure sounds good.

The North-South pole attraction for parallel current flow explanation is exactly what I think is true.

The question that follows is:
If a current flow produces a magnetic field (actually an EM field), then does that mean that a solid magnet (natural lodestone mineral or an electomagnetized magnet) has some sort of electric current? Is there a current flow within the static magnet? Is that current due to synchronized electron spins?
...

 

[employee #416]

Metallicbeing, when you are referring to the spinning of electrons, are you referring to their spin in the orbitals? Could you provide me a link stating this also? It sounds interesting.

 

[pervect]

The North-South pole attraction for parallel current flow explanation is exactly what I think is true.
...

This explanation would not properly explain the observed deflection of an electron beam in a cathode ray tube. The Lorentz force law correctly predicts that the force on a moving electron inside a CRT increases with the velocity of the electron ( F=q(v x B) ). An attempt to explain deflection of an electron beam based on its magnetic moment will fail because

1) it wouldn't give a large enough force to match observed results
2) it wouldn't give a force proportional to velocity
3) it would predict that an electron beam would have to generate two spots on the screen, one spot for each orientation of the magnetic moment, like the stern gerlach experiment does with silver ions.

In actuality, we observe the forces due to the magnetic moment of the electron are so small that they do not resolve the spin of the electron, the Lorentz force by far dominates any force due to the magnetic moment.

 

[Metallicbeing]

The North-South pole attraction for parallel current flow explanation is exactly what I think is true.

The question that follows is:
If a current flow produces a magnetic field (actually an EM field), then does that mean that a solid magnet (natural lodestone mineral or an electomagnetized magnet) has some sort of electric current? Is there a current flow within the static magnet? Is that current due to synchronized electron spins?
...

In everyday materials, electron spins are randomly orientated, leaving no organized field. Permanent magnets were created in the presence of a magnetic field while they were in viscous form then allowed to solidify. It would seem that only ferrous type materials are capable of keeping a synchronized spin with no electron current flow present. If there is any current flow at all, then it would be in the form of small eddy currents.

 

[Metallicbeing]

Metallicbeing, when you are referring to the spinning of electrons, are you referring to their spin in the orbitals? Could you provide me a link stating this also? It sounds interesting.

I'm sorry. I read this some time ago. Maybe you can google it under "What is magnetism". If I recall correctly, that's how I found it.

 

[what_are_electrons]

This explanation would not properly explain the observed deflection of an electron beam in a cathode ray tube. The Lorentz force law correctly predicts that the force on a moving electron inside a CRT increases with the velocity of the electron ( F=q(v x B) ).

The CRT involves just a single beam of electrons, so I don't quite seen the connection. Am not that familiar with Lorentz law as applied to free electrons in UHV.
Correct me if I'm wrong, but wouldn't free electrons in a CRT act different from the free charges flowing in two wires that have equal currents? Don't the actual electrons move very slowly in wires (ca. cm/sec) not 10e7 m/s like free electrons in the CRT?

An attempt to explain deflection of an electron beam based on its magnetic moment will fail because
1) it wouldn't give a large enough force to match observed results
2) it wouldn't give a force proportional to velocity
3) it would predict that an electron beam would have to generate two spots on the screen, one spot for each orientation of the magnetic moment, like the stern gerlach experiment does with silver ions.

Since we are talking about charges moving in wires vs electrons moving through space, can we apply the same laws?

The Stern-Gerlach experiment is an interesting experiment, but it may be that other factors were at work in that experiment. Why is it they used a beam of Ag atoms (not ions as you suggest)? Silver in atomic form has a 4d9, 5s2 electron configuration, only one unpaired electron in a nearly filled shell.

My 1985 2nd edition of Polarized Electrons by J. Kessler (Springer Verlag) states on p2:
"Conventional spin filters, the prototype of which is the Stern-Gerlach magnet, do not work with free electrons. This is because a Lorentz force, which does not appear with neutral atoms, arises in the Stern-Gerlach magnet. This, combined with the uncertainty principle, prevents the separation of spin-up and spin-down electrons."

This book includes discussions on obtaining polarized electrons from unpolarized materials, generating polarized light from polarized electrons etc. Quite fascinating.

In actuality, we observe the forces due to the magnetic moment of the electron are so small that they do not resolve the spin of the electron, the Lorentz force by far dominates any force due to the magnetic moment.

 

[pervect]

I've posted some of the equations relative to dipoles and the forces on and between them in another thread, because I thought they might be interesting and it was something constructive.

You are absolutely right that a free electron cannot be separated out by a Stern-gerlach type experiment. This is a somewhat obscure point that not many people know about, it originated with (I believe) Bohr. As far as whether or not the experiment used ions, or atoms, I think you're probably right about it using atoms, but I didn't find a definitive reference.

I missed the most obvious reason that the electron spin explanation won't explain a CRT- a magnetic dipole only expeiences forces from a changing B field, not a static B field. Obviously, static magnetic fields do affect the electron beam in a CRT. If you have one you're not terribly fond of, you can even try putting a magnet near the CRT and watch what it does to the beam. But don't blame me if it messes up the focus and resolution :-).

A wire contains a lot of slowly moving charge, the electron beam contains fewer but faster moving charges. The wire also contains stationary charge, which eliminates the electric field. However, there is no force on the stationary charges due to a magnetic field, so they can be ignored.

The Lorentz force gives the force on a single moving charge is F = q(E + v x B).

If we have a wire with an area A and length L, the current will be n*e*v_d*A, where n is the electron density / unit volue, see

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html

The product of the current and lenght, I*L will be

n*A*L*e*v_d

So we expect the Lorentz force on a wire of length L carrying a current A to be the force on a single electron with a velocity of v_d, multiplied by the number of electrons in the volume A*L, which is n*A*L

i.e.

F = (n A L) * e * v_d * B

This can be re-written as

or F = I * L * B

This is exactly the result from
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/forwir.html#c1

 

[robphy]

Another way to look at it is that currents obey an inverse square law, just like masses and charges.

It's just, because currents are vectors instead of scalars, you have to use the dot product instead of ordinary multiplication.

$$\vec{F} = C \frac{\vec{I}_1 \cdot \vec{I}_2}{|\vec{r}|^2} \hat{r}$$

I forget what the constant C should be, but it's negative.

The force should be inverse-linear.
http://spiff.rit.edu/classes/phys313/lectures/amp/amp2_f01_long.html
http://theory.uwinnipeg.ca/physics/mag/node10.html

 

[Integral]

Simple fact.
Over the last 3 or 4 centuries mankind has been observing the interactions of magnetic fields. Work done by Faraday, Ampere, Oersted, Coulomb and others was tied together in a very nice Mathematical package by Maxwell in the 1860,s. Using these mathematical formalities we are able to predict with precision the amount of force generated by current carrying wires and other Electromagnetic and Electro Mechanical interactions. What Physics does not do is provide a answer to the question WHY. All of physics is based on OBSERVATIONS of the physical universe, all of our mathematical models are based on these observations. We have observed that current carrying wires can attract each other or repel each other based on the relative direction of the currents in the wires. We have the Mathematical models to calculate the results but there is answer to the question why.

If you wish to pursue the WHY question please start a thread in the Philosophy forum.

 

[Hurkyl]

The force should be inverse-linear.

An inverse-square force field emitted by an infinitely long rod dies off at an inverse-linear rate.

 

[da_willem]

As much as Integral is right, you can always try to 'explain' such things by deriving it from more fundamental principles. Ofcourse this only shifts the 'why' to other observations. But this is most of the times felt as an answer to the question, and is satisfactory as such.

Maybe this is a satisfactory way of looking at it. It only needs SR and Coulombs law of attracting opposite charges:

You can think of an electricaly neutral current carrying wire as consisting of a negative line element moving (lets say) to the right superimposed on a positive line element moving to the left. A positively charged particle moving with a certain speed to the right 'sees' both line elements Lorentz contracted, and thus having a larger charge density. But because the Lorentz contraction is larger for the negative line element because of the larger relative speed in the particle sees an net negative charge! The moving particle (and also another current carrying wire, depending on the direction the current flows!) will be attracted to the wire.

So an electrically neutral wire in one frame is charged in another, and a magnetic field in one frame is an electric field in the other.

 

[pervect]

Maybe this is a satisfactory way of looking at it. It only needs SR and Coulombs law of attracting opposite charges:

I've found that this explanation, while absolutely correct, unfortunately tends to severely confuse people who haven't yet learned to calculate forces with the Lorentz force law.

 

[da_willem]

Mathematically this works out quite well too:

Consider the S' frame comoving with the charged particle at a speed u. And let's say the current flows with a speed v. So The line charge 'seen' from the S frame (in rest relative to the wire) is also Lorentz contracted so: $$\lambda=\gamma\lambda_0$$

As I said the net charge seen by the moving charge is proprtional to the difference in Lorentz contraction or the difference in $$\gamma$$ so $$\lambda_{net}=\lambda_+-\lambda_-=\lambda_0(\gamma_+-\gamma_-)$$. With a little algebra this difference can be shown to be:

$$\frac{-2\gamma uv}{c^2\sqrt(1-u^2/c^2)}$$

By using the above and the formula for an electric field of a line charge at a distance $$s: E=\frac{\lambda_tot}{2\pi\epsilon_0s}$$
The electrical force on q in S' is:
$$F'=qE=-\frac{\lambda v}{\pi \epsilon_0 c^2s} \frac{qu}{\sqrt{1-u^2/c^2}}$$

In S this becomes using the (relativistic) transformation formulas for forces:
$$F=\sqrt{1-u^2/c^2}F'=-\frac{\lambda quv}{\pi\epsilon_0 c^2 s}$$
Or in terms of the current $$I=2 \lambda v$$:
$$F=-qu\frac{\mu_0 I}{2\pi s}$$

If you change the charge by another line element you would obtain the force per unit length by replacing q by $$\lambda$$. Another (negatively charged) line element moving with the same speed u the other direction would produce the same (attractive) force. But what we have now are two current-carrying wires a distance s apart. The current of the second wire is $$I_2 =2 \lambda u$$. So the force per unit length has become (by replacing qu with $$I_2$$):
$$F=\frac{\mu_0}{2\pi}\frac{I_1I_2}{s}$$

Exactly the same as can be obtained by using magnetism!

NB: the relativistic Lorentz contraction is only very small, because the charges move at nonrelativistic speeds, but because there are so many charges it produces a noticable effect.

NB2: For more details see paragraph 12.3.2 of Griffith's "introduction to electrodynamics"

 

[what_are_electrons]

Simple fact.
Over the last 3 or 4 centuries mankind has been observing the interactions of magnetic fields. Work done by Faraday, Ampere, Oersted, Coulomb and others was tied together in a very nice Mathematical package by Maxwell in the 1860,s. Using these mathematical formalities we are able to predict with precision the amount of force generated by current carrying wires and other Electromagnetic and Electro Mechanical interactions. What Physics does not do is provide a answer to the question WHY. All of physics is based on OBSERVATIONS of the physical universe, all of our mathematical models are based on these observations. We have observed that current carrying wires can attract each other or repel each other based on the relative direction of the currents in the wires. We have the Mathematical models to calculate the results but there is answer to the question why.

If you wish to pursue the WHY question please start a thread in the Philosophy forum.

Metallic Being provided the type of answer that matches the question originally posed. My response to his answer was: "The North-South pole attraction for parallel current flow explanation is exactly what I think is true."

But in the following, I briefly address the topic posed:
A "Why" question can be interpreted in various ways. It is often posed by people, from a very young age to an old age, who want to learn and to understand what they are seeing. A "Why" question can be interpreted and answered in various ways. A " Why" question might mean: What is the cause of...? or it might mean: How does this happen? Since this forum is mainly populated by intelligent students of physics and closely related subjects, we should assume they can handle either formula based answers or word based answers. So, unless we ask for more detail on the question, we will not know if we are or are not providing a suitable answer. Such is the nature of communication.

Personally speaking, philosopy is a way of thinking about different subjects which should be taught to college students, but is seldom done so, and I have no intention to ask any philosophical questions within this forum.

 

[pervect]

It's interesting that you like rather vaguely worded statements about "synchronized electron spin", whatever that's supposed to mean, as opposed to statements like "the force on a current carrying wire is $$I L \times B$$, where I is the current, L is the length of the wire, and B is the magnetic field.

I'm a bit curious - can you provide some insight into why you found Metallic Being's "explanation" so attractive, while you apparently aren't interested in the formulas which numerically describe the behavior of currents and fields?

Formulas, I might add, that you can look up in any physics book, or, if you don't have a physics book handy, on any of the numerous websites on electromagnetism hosted by various colleges?

 

[what_are_electrons]

It's interesting that you like rather vaguely worded statements about "synchronized electron spin", whatever that's supposed to mean, as opposed to statements like "the force on a current carrying wire is $$I L \times B$$, where I is the current, L is the length of the wire, and B is the magnetic field.

I'm a bit curious - can you provide some insight into why you found Metallic Being's "explanation" so attractive, while you apparently aren't interested in the formulas which numerically describe the behavior of currents and fields?

Formulas, I might add, that you can look up in any physics book, or, if you don't have a physics book handy, on any of the numerous websites on electromagnetism hosted by various colleges?

Based on context, your response is aimed to me, the thread author. Did not say I liked or disliked the phrase "synchronized electron spin". But now that you highlight it, it is an interesting way, and a very common way, to perceive or to image the atomic level cause (source) of the "ferromagnetism" in Fe, Co and Ni at RT. I am, however, open to other perceptions or forumula that explain ferromagnetism at the atomic level. It would be fantastic if those perceptions or formula would also explain the anti-ferromagnetism of Mn and Cr.

His simple and obvious terminology (N-S interaction) immediately provides an easy-to-grasp picture of what is happening and what can be explained by formula. This type of mental image or picture is an extremely valuable tool for either self-learning or for teachers. No, I'm not a teacher. Yes, I am learning from you as fast as I can but I'm behind in the formula end of physics. That does not hinder me from understanding concepts and perceptions and pictures that relate to observable phenomena. I am very much in favor of providing some sort of mental image/picture together with formula whenever possible. Such images greatly improve communication, but are difficult to do in this forum unless we have a white (scratch) board.

His N-S explanation matches my interpretation of that phenomenon. My interpretation of that phenomenon, and also Hunds's rule, is based on my current understanding of the internal structure of the electron, which is the most important elementary particle in the universe, except for the proton (which is not really an elementary particle). I say that because the universe in 90% hydrogen and all other matter is derived from hydrogen. It is an important particle, and has been studied in great detail, and yet we do not even know its size. Many do not even know that it is a minature electromagnet in the sense it has both an electric field and a magnetic field even when it is at rest, if could ever be at rest.

Many of my questions to the members of this forum are aimed at understanding and revealing the fundamental structure and nature of the electron and to some extent also the photon because photons can transfer energy from one electron to another electron.

 

[Metallicbeing]

It's interesting that you like rather vaguely worded statements about "synchronized electron spin", whatever that's supposed to mean, as opposed to statements like "the force on a current carrying wire is $$I L \times B$$, where I is the current, L is the length of the wire, and B is the magnetic field.

I'm a bit curious - can you provide some insight into why you found Metallic Being's "explanation" so attractive, while you apparently aren't interested in the formulas which numerically describe the behavior of currents and fields?

Formulas, I might add, that you can look up in any physics book, or, if you don't have a physics book handy, on any of the numerous websites on electromagnetism hosted by various colleges?

Ease up Pervect. It's just something I read. If they want to investigate it further, they will. Don't be such a science nazi.

 

[krab]

My response to his answer was: "The North-South pole attraction for parallel current flow explanation is exactly what I think is true.".

..and is exactly why your understanding of magnetic phenomena is limited. A wire carrying current does not have North or South pole, and yet is attracted to another such wire, by the magnetic field it generates. North-South pole attraction is a simple way of understanding mechanical interaction between bar magnets. In the case of a general magnetic field, it is not all that enlightening.

 

[pervect]

Ease up Pervect. It's just something I read. If they want to investigate it further, they will. Don't be such a science nazi.

Sorry to pick on you, your post had enough disclaimers in it to alert almost anyone that you were speculating wildly.

 

[Metallicbeing]

North-South pole attraction is a simple way of understanding mechanical interaction between bar magnets.

...and if you took a powered electro-magnet, you can determine which end is the same as North or South compared to a bar magnet. You're right, there is no permanent North or South pole on an electro-magnet (or wire), but it helps to visualize the concept. Sorry, it's not always perfect.

Why would you try to explain to somebody who knows little or nothing about this subject in a way they might only understand after a few years of college? First they need to grasp the concept. The math comes later.

 

[Metallicbeing]

Sorry to pick on you, your post had enough disclaimers in it to alert almost anyone that you were speculating wildly.

I understand the importance of math. Unfortunately, not everyone speaks "Mathematician". Don't you want to help people (layman) understand? It's one thing to descibe your variables, but you need to tell others (who haven't kept up on their math) what it all means. If you can't do that, then that is where you're lacking.

 

[what_are_electrons]

..and is exactly why your understanding of magnetic phenomena is limited. A wire carrying current does not have North or South pole, and yet is attracted to another such wire, by the magnetic field it generates. North-South pole attraction is a simple way of understanding mechanical interaction between bar magnets. In the case of a general magnetic field, it is not all that enlightening.

Hmmm. Most of the phenomena found in atomic and quantum physics at the most fundamental level appear as discrete binomial or trinomial systems (eg +/- electron-proton up-down UUD DDU particle-antiparticle N-S super-symmetry...) so I do not take offense at your inference, in fact, it is a compliment since I am focusing on the fundamental nature of particles not their macroscopic phenomena which are described by Maxwell, Faraday, Lorentz, Gauss and many others.