Why do current carrying wires attract

Your question is assuming that the electrons are weakly interacting with the nucleus. The interaction with the nucleus is extremely strong. It is better to ask instead why do we have conductivity at all. Electrons are so tightly bound to nuclei of atoms, why should a tiny external electric field get them moving? The answer is that quantum mechanical effects can spread out electrons over many atoms. This is responsible for chemical bonding.

In metals, the electrons have a spread out wavefunction, and the energy-band of spread-out electron states is only partly filled, so it only takes a little bit of energy to push an electron into motion.

But for your original question, there is an easy way to see the answer. Consider two infinite charged wires 1 cm apart. You know that they repel, so they move apart. Now boost to a frame moving along the wires at a huge speed, near the speed of light. Relavistic time dilation slows down the rate at which they move apart.

But the charge density has gone up in this frame, because of the length contraction. So there must be an additional attractive force due to the currents in the wires. In the limit that you are moving at the speed of light, the attractive like-current force must exactly cancel the repulsive like-charge electrostatic force. With two currents flowing in opposite directions you can determine that the magnetic fields are in the same direction and will therefore repel.

When the currents flow in the same direction the magnetic field will be opposite and the wires will attract. Like a lot of explanations in science, there is the simple one derived hundreds of years ago, and a more complex model that gives the same answer but requires you to understand more advanced topics and mathematics.

Read on if you dare. You can also work this out using relativity and not require a magnetic field. In the frame of reference of the moving charges they will see a length contraction of the universe along the direction of travel.

If electrons in both wires are moving in the same direction they see the same number of electrons in the other wire because they are moving at the same speed. But they see more protons. Notice a stream of yellow electrons traveling through the circuit; flowing as they always do from negative to positive — opposite the direction of conventional current. To halt the flow of current, click on the red Stop button or the knife switch.

Clicking the blue Pause button will let you examine the process in mid-stream. As you can see, the wires in the series circuit repel one another, while the wires in the parallel circuit attract one another. This is explained by the right hand rule , which helps visualize how a magnetic field depicted by the blue field lines above around a wire travels. If the current direction is parallel to the magnetic field, then there will no force on the conductor exerted by the magnetic field.

A B-field exerts force on a moving charge, in a direction perpendicular to the B field. A B-field exerts force on a moving charge, in a direction perpendicular to the motion of the charge. By similar reasonong to above, this also means the force must be zero when B and the velocity of the charge are parallel. When a current carrying wire is placed in a magnetic field, it experiences a mechanical force.

And the force will be maximum if the current carrying wire is placed in a direction perpendicular to that of the magnetic field.