# Why do two wires with currents in the same direction attract?

1. Dec 6, 2010

### bkiag

I understand that using F = qv x B and the fact that positive currents generate counter clockwise magnetic fields, it can be concluded that two parallel wires carrying currents in the same direction attract.

But what about when you think about it in the frame of reference of the charges in the wire? If you imagine that the charges are still and the wires are moving, then there are two lines of charge with equal polarity. Shouldn't they repel? As for currents moving in opposite directions, you could imagine a negative current (electrons, perhaps) moving the same direction as a positive current (hydrogen ions, perhaps). In the frame of reference of the charges, they would attract. However, according to EM theory, they repel. What am I missing here?

2. Dec 6, 2010

### tiny-tim

welcome to pf!

hi bkiag! welcome to pf!
you've forgotten that wires are neutral!

in the new frame of reference, there's now two lines of positive charge moving in the same direction …

these "positive currents" attract, and the wires themselves are neutral, so make no contribution to the force

(there's a cool site somewhere that gives a detailed description of how to get the current force directly from the Lorentz transformations, with diagrams, but i can't remember where it is )

3. Dec 6, 2010

### bkiag

Re: welcome to pf!

Thanks for the response!

Like charges repel, no?

I'm not sure if my question was stated clearly. Maybe if I give an analogy...

Two cars are driving down the highway next to eachother. Each car represents a current and each car has a positive charge. If you're sitting in one of the cars and you look out the window at another car driving in the same direction, it appears as if it is not moving. Since each car is a positively charged, shouldn't they repel? Like charges repel.

4. Dec 6, 2010

### tiny-tim

yes, but to keep the analogy, each lane of the the road must have a negative charge, so each lane-plus-car is neutral, and will not repel the other

5. Dec 8, 2010

### compter

The total amount of charge remains zero for both wires. The fact that charges is moving leads to a relativistic effect, causing the Lorentz force.

6. Dec 10, 2010

### wheelatharm

The basic thing you have wrong is the common misconception that electrical current is charge flowing through a wire like water through a pipe.
DC electrical current through a wire is more like having two rows of people facing each other down a long hallway. The people in each row have hands interlinked with each other, and one row is the electrons, the other row are the protons. There are exactly as many people in each row with the same charge, so there is never at any time any net charge. While the people in any row would be either attracted or repelled from people in a hallway next door, the other wire, there will be complete cancellation of force from the sum of all the people in each set of rows. This is what being neutrally charged means, each charge is always cancelled.
By the way, the people in each row have extra sets of hands that let them grab on to the people opposite them in the hall.
When current flows, it gets the people in one row, electrons, vibrating. These vibrations can transmit energy without anyone ever breaking hands. Much the same way that if the people in one row were being bounced around on one end, they could become passive and start moshing around to where they just transmit the energy that they get from one end to the other.
In a DC circuit, every once and a while the row of electrons moves down a bit. They people change hands with the people across from them, and shift down a bit.
In an AC circuit, the rows never really move and the electrons stay in one place.

This is why there is no electrical repulsion between the wires, as stated before they are electrically neutral, and there are no packets of net charge to create a force.

m

7. Dec 11, 2010

### tiny-tim

many hands make light work!

8. Dec 12, 2010

### compter

Acording the contraction theory it seems that the density of moving electrons with respect to each other becomes higher. That all and explains the excistings of the magnetic field. The magnetic field is a kind of derivative of the force acting between charged bodies.