Magnetic field and repulsion bewteen wires

[gralla55]

If you place a wire with a running current in a magnetic field, the magnetic field will exert a force on the wire. So, if you place two wires parallel to each other, the current on each will produce a magnetic field, which in turn will attract or repulse the other wire depending on the direction of the current.

What I don't get, is how the magnetic field from wire a reaches wire b. If you look at drawings of magnetic field lines between wires, the total field does not seem to run through the wires at all, as the magnetic field generated from wire a, "deflects" the field generated by wire b.

This is what I'm talking about:

What am I missing?

 

[mfb]

You still have some field inside, but you have to draw more lines close to the wires to see it.
Alternatively, consider the field as superposition of the fields of the individual wires - that makes it easier to see.

 

[technician]

The best way is to think about the magnetic fields interacting. The field due to wire a does not have to reach wire b..
It reaches the field due to b.
Faraday had a great way to describe magnetic fields:
1) they can be represented by lines of force
2) the lines of force behave like stretched elastic bands
3) lines of force cannot cross each other
Look at your diagrams and imagine those lines as stretched elastic bands... Do you see the attraction and repulsion??

 

[gralla55]

Thank you both, that really helped!

 

[jtbell]

The best way is to think about the magnetic fields interacting.

The fields do not interact. They superpose (add).

The field due to wire a does not have to reach wire b.

How does this fit in with $B = \frac{\mu_0 I}{2 \pi r}$ ?

 

[technician]

Superposition is a form of interaction ?
Adding is an interaction ?
Semantics?

 

[WannabeNewton]

Superposition is a form of interaction ?
Adding is an interaction ?
Semantics?

It is not semantics. Superposition works because the various fields being superposed act independently of each other hence there is no interaction amongst them. If the fields were interacting with one another, why in the world would you be able to just simply add them up to get a net field? There would be interaction terms to take into account.

 

[mfb]

Superposition is the non-interaction of two things at the same place: You can consider them individually, without any cross-terms from an interaction.

Edit: Same minute.

:cookie:

Still faster than LastOneStanding :p

 

[WannabeNewton]

Superposition is the non-interaction of to things at the same place: You can consider them individually, without any cross-terms from an interaction.

Edit: Same minute.

Beat you to it, where's my cookie

EDIT: I have received my cookie, hooray!

 

[VantagePoint72]

Superposition is a form of interaction ?
Adding is an interaction ?
Semantics?

Linear superposition is not a form of interaction. Interaction implies something acting on another thing. When two electric or magnetic fields are superposed, they don't do anything to each other. Two electromagnetic waves will just pass through each other unchanged. Classical electric fields do not interact with other electric fields: they interact with charged particles.

I've never understood why people will dismiss a disagreement as "semantics" in the tone that implies they're thinking "trivial". Semantics means "meaning". You are using words in ways contrary to what they mean. That's hardly trivial.

 

[VantagePoint72]

Still faster than LastOneStanding :p

Not fair! Mine included an extra side remark on language usage! Hmph.

 

[technician]

Implies?...
Isn't this subjective?

 

[BruceW]

I've never understood why people will dismiss a disagreement as "semantics" in the tone that implies they're thinking "trivial". Semantics means "meaning". You are using words in ways contrary to what they mean. That's hardly trivial.

Ah, Semantics. Now the problem is who decides what is the absolute meaning of a word? And how strictly it must be adhered to. I personally would not use the word 'interaction' to describe linear superposition. But also I wouldn't be totally against other people using the word in that way.

I think the most important thing is that if you are unsure what definition someone is using for a particular word, then you need to ask them. And conversely, if you are using a definition for a word which is not the most common one, then it is common courtesy to give a brief explanation. For example, I will often say something like "in the sense that"

 

[BruceW]

What I don't get, is how the magnetic field from wire a reaches wire b. If you look at drawings of magnetic field lines between wires, the total field does not seem to run through the wires at all, as the magnetic field generated from wire a, "deflects" the field generated by wire b.

that's a good point. To start with, if we just have one wire (let's say wire B), then if we take the limit of a very thin wire, the magnetic field just outside of the wire (due to itself) will tend to infinity. Then if we add wire A to the system, the magnetic field just outside of B will only change a tiny bit (compared to before). This is why the field is pretty much circular around either of the wires. But the crucial point is that for any wire with finite size, the magnetic field just outside of wire B will change by a non-zero amount due to the introduction of wire A. In other words, the field won't be exactly circular around the wire. and, if you were able to look closely enough to see the wire, the magnetic field actually does pass through it.

So, you can resolve the 'problem' by thinking about the wires having nonzero width, and taking the limit of that width being very small, but still not zero. This is an example of a "singular perturbation problem", which I was reading about the other day. It is very common throughout physics.

also, if the problem has wires of finite width (i.e. you are not trying to approximate very thin wires), then there is no problem, since you will be able to see macroscopically that the magnetic field will simply not be circular around the wires.