E&M wire attraction

Apologies if this is being posted in the wrong section! this is just a side thought I came across, it is not HW.

In learning about magnetism, I know that a changing current in a wire creates a magnetic field. So why are wires in our homes/ anything with wires close together not constantly attracting or repulsing each other?
At first I thought this was because they are not changing except when turned on/off which is such a small amount of time that the B field is negligible. But then I remembered that most homes have AC which is constantly changing anyways.

jtbell
Mentor
a changing current in a wire creates a magnetic field.

Actually, any current, whether constant or changing, creates a magnetic field.

So why are wires in our homes/ anything with wires close together not constantly attracting or repulsing each other?

They are! However, these forces are too small to be noticeable under everyday conditions.

Ok, can see why household wires have negligible effects. But what about wires carrying large currrents, like power lines?

jtbell
Mentor
Distribution lines carry larger voltages and therefore smaller currents for equal amounts of power. The lines running along your street probably carry more current than a typical circuit in your house, but not by as much as you would expect if the voltages were equal. I haven't actually worked out the numbers myself, but it would be a nice exercise to find out the typical currents in those lines, and the typical spacing between them (1 m for neighborhood distribution lines?), and calculate the force per length of wire.

It also might make a difference that the usual formulas for magnetic fields and forces assume constant currents, whereas electical power systems are AC. The average force between two parallel wires probably depends on the relative phase of the currents in them.

robphy