Applying the left/right hand rule to a wire with current

[thisischris]

Hi there.

I'm basically trying to understand why when 2 wires are place near each other, given a current in the same direction they will attract each other.

I have read a this: https://www.physicsforums.com/showthread.php?t=39472

But I don't see how some say 'generates a magnetic field upwards(to the ceiling)'. Surely it would be generating this in all perpendicular directions. And not just one 'instance' of pointing upwards?

Hope that's clear enough, if not I'll try draw a diagram.

 

[tiny-tim]

welcome to pf!

hi thisischris! welcome to pf!

But I don't see how some say 'generates a magnetic field upwards(to the ceiling)'. Surely it would be generating this in all perpendicular directions. And not just one 'instance' of pointing upwards?

this is two horizontal wires

any current-carrying wire generates a magnetic field whose field lines are circles around the wire, with the arrows all going clockwise (say)

so if there's another wire to the left, the arrow on the circle that cuts it will be pointing up (but if there's another wire to the right, the arrow on the circle that cuts that wire will be pointing down)

 

[sophiecentaur]

I think what that explanation you read is approaching it this way: start with the field for one wire at the place where the other wire happens to be (hence 'upwards'). It will be downwards on the other side of the wire but that's of no interest here.
You then use the upwards for the magnetic field direction and the direction of the current along the second wire to give you a force in the appropriate direction.
If you were to take the OTHER wire to start with, the B field will be downwards so the force will be in the opposite direction - So it works and it's consistent and also happens to show that the forces must be equal and opposite (Newton's Third Law rules here also)

 

[thisischris]

Uhhhaaaaaaaaaaaaaaaaaaaaaaaaaaaaaah! I think I got it!

Could anyone have a look a look at my diagram I drew (amazing product of procrastination!), and just let me know if I have applied it correctly?

 

[tiny-tim]

wow! long spring break!

yes that looks fine ​

(i assume your snaily spiral is just you being artistic, and you know that the field is really circles? )

 

[sophiecentaur]

The brilliant thing is that you can choose the other wire as providing the field and then the force on the 'current carrying' wire is just right, too.

 

[thisischris]

(i assume your snaily spiral is just you being artistic, and you know that the field is really circles? )

Whooops. Thank you!

The brilliant thing is that you can choose the other wire as providing the field and then the force on the 'current carrying' wire is just right, too.

I'm not too sure on what you are describing/clarifying, are you saying that both provide a magnetic field which acts on the other and hence both attract each other?

 

[sophiecentaur]

Whooops. Thank you!



I'm not too sure on what you are describing/clarifying, are you saying that both provide a magnetic field which acts on the other and hence both attract each other?

In your diagram you 'chose' one wire to provide the field and the other wire had the current so you apply IXB for the force. I'm saying that you get the same answer if you choose it the other way round. But this is just one way of looking at things. You can explain the force between current carrying wires without invoking magnetism at all.

 

[thisischris]

In your diagram you 'chose' one wire to provide the field and the other wire had the current so you apply IXB for the force. I'm saying that you get the same answer if you choose it the other way round. But this is just one way of looking at things. You can explain the force between current carrying wires without invoking magnetism at all.

Cheers. Right, would you mind explaining how you would without 'invoking' magnetism?

 

[truesearch]

Are you familiar with the shape of the magnetic field around a current carrying wire?...concentric circles.
Do you know what the combined field of 2 current carrying wires looks like (currents in same direction; currents in opposite directions). The shape of these field lines fit well with the attraction and repulsion of current carrying wires in much the same way as the field pattern between N and S and N and N poles fit with attraction and repulsion.
The concept of fields, represented by lines of force, is central to understanding many other aspects of physics. Faraday came up with the idea and it is 'text book' physics.

 

[sophiecentaur]

Cheers. Right, would you mind explaining how you would without 'invoking' magnetism?

If you can accept that the numbers involved in the following actually manage to give the right answer, then here goes.
The average drift speed of electrons in a wire is only about 1mm/s but it is enough to produce a measurable RELATIVISTIC effect. (Bear with me: there are an awful lot of free electrons in a piece of wire so the effects all add up)
Imagine you are sitting on a positively charged metal ion in one wire. You will see a lot of other stationary positive charges in the other wire with a certain average spacing between them. You will also see an equal number of electrons moving past you. Because they are moving, relativistic effects will make them appear closer together than the stationary ions (more densley packed). There is, thus, an imbalance in what you see, with more negative charges than positive charges. Hence an attraction.
Now imagine you are on a moving electron in one of the wires. You see a load of electrons, moving along with you, in the other wire and an equal number of positive ions, moving relative to you, so more densely packed positive charges because of relativity. Again, the net imbalance produces attraction.
So, without needing to consider any magnetic fields, we have accounted for an attractive force between the wires. If you put the actual values into the equations, you get exactly the same force from this method as you get from the conventional (magnetic- based) calculation.

The argument works just as well for when the currents are in opposite directions, too.

Ain't that fascinating? Who needs Magnetism? It does show how many things aren't 'really' where - they are just constructs in our heads to help 'explain' things.

 

[sophiecentaur]

Actually, the above needs a modification / clarification. When I say "and equal number of", this is not strictly correct. There are MORE of the opposite charges in a given section of the 'other wire'. (In both of the cases discussed)

 

[truesearch]

describing magnetic effects using a relativistic approach is great. The best analysis that I have seen is in a textbook by OHANIAN... called Physics for engineers if I remember correctly. Clearly explained and mathematically quite straight forward to follow.

 

[sophiecentaur]

And you can keep both hands free! ;-)

 

[truesearch]

No comment !

 

[thisischris]

The argument works just as well for when the currents are in opposite directions, too.

Ain't that fascinating? Who needs Magnetism? It does show how many things aren't 'really' where - they are just constructs in our heads to help 'explain' things.

Thank you for response. Not that I understand it that well (I haven't studied relativistic effects), although I don't think I need to at this level. Much appreciated!

 

[sophiecentaur]

Thank you for response. Not that I understand it that well (I haven't studied relativistic effects), although I don't think I need to at this level. Much appreciated!

All you need to do is appreciate that, when things are moving relative to you, they appear closer together. (The Lorentz Contraction). Normally we would think of this only happening when things are going really fast but it is always there when there is relative motion - however small.
This alternative explanation is a typical example of what we think is 'real' being only the way we look at things.