AC through the wires, forces acting in/out of phase currents

[moenste]

Homework Statement

Two parallel wires have currents passed through them which are in the same direction. Draw a diagram showing the directions of the currents and of the forces on the wires.

Alternating currents are now passed through the wires. Explain what forces would act if the currents were: (a) in phase, and (b) out of phase, by π rad.

2. The attempt at a solution
For the drawing part:

We have two wires that have upwards directed current. The X circles represent the entering of the field into the paper and O circles represent the field coming out of the paper. We also have smaller circles that represent the field of the other wire that is affecting the neighbouring wire.

The forces are acting to the center of the distance between the wires.

In terms of (a) and (b) I don't understand what should be done. AC means that the current switches back and forth. What does it mean "current in phase" and "current out of phase by π rad"? What forces would be acting? Don't think that the question is about the gravity forces or something like that...

 

[BvU]

Can't say I find the smaller circles clarifying things ...

"In phase" means the alternating currents go upwards and downwards synchronously. So if one is $\ \sin \omega t\$ the other is also $\ \sin \omega t\$.

"Out of phase" here means completely out of phase: when one goes up the other goes down and vice versa. So if one is $\ \sin \omega t\$ the other is also $\ \sin ( \omega t\ + \pi) = - \sin \omega t\$

 

[moenste]

Can't say I find the smaller circles clarifying things ...

The smaller circles represent the field of the other wire (of the second on the first and the other way around). For example: we have a wire II with B coming out of the paper on the side of the I wire. And this B is not only limited to the distance between I and II, but this field is affecting the whole left side of the area. However, the larger is the distance from II, the less powerful is the field. It is taken from this video.

"In phase" means the alternating currents go upwards and downwards synchronously. So if one is sinωt \ \sin \omega t\ the other is also sinωt \ \sin \omega t\ .

"Out of phase" here means completely out of phase: when one goes up the other goes down and vice versa. So if one is sinωt \ \sin \omega t\ the other is also sin(ωt +π)=−sinωt

Hm, so the centripetal force will act?

 

[BvU]

Hm, so the centripetal force will act?

There is no circular motion here: the sine is just a way to describe the time dependence of the current

 

[moenste]

There is no circular motion here: the sine is just a way to describe the time dependence of the current

But what forces are they talking about then? There is no mentioning of any forces in the Wikipedia article.

 

[BvU]

They are talking about the magnetic force on a current carrying wire in a magnetic field (basically the Lorentz force)

The wikipedia article was about phase