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I've learnt that any current carrying wire produces a magnetic field around it. Also two wires carrying current in the same direction attract each other, whereas, two wires carrying current in opposite directions repel each other.

We know that power lines which distribute power from the power station carry alternating current. So, I the direction of magnetic force between the lines vary with time and I expect the lines to swing along its transverse direction. But whenever I look at overhead power lines, they look so stable. Why don't they swing as in this MIT video? I suspect the magnetic forces due to the current is significant enough when compared to the mass of the cables.

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    $\begingroup$ Wire on a bundle on the same circuit need spacers like this and this because in case of a lightning strike the current increases to the point where the two wires slam against each other and destroy themselves. $\endgroup$
    – John Alexiou
    Feb 24, 2020 at 0:31

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Electrical power lines can attract and repel each other, but the amount of force involved is incredibly small under most common conditions. Current in two wires flowing in the same direction attract each other, and currents in opposite directions repel. The magnitude of this force over a wire of length L (assuming the currents in each wire are equal) is

$$F=\frac{\mu_0 I^2 L}{2\pi d}$$ where:

-$\mu$ is called the permeability of free space (1.26*10-6 Newtons/Amp2)
-I is the current in the two wires
-L is the length of the wire (meters)
-d is the distance between the wires (meters)
-F is the resulting force in Newtons, which can be converted to pounds of force by multiplying by 0.225.

To take an example typical of a high power kitchen appliance like a water kettle, the current in the two wires going to the outlet in the wall is about 10A, and the distance between them is about 5mm. Over a 1 meter wire length the force is only 0.004 Newtons, which is a bit under one thousandth of a pound, so it's very small!

So you can see that for pretty much any case in day to day life electrical wires will attract and repel each other, but it will be unnoticeable because it is so small. One case where these forces matter is in high-powered electromagnets, like the superconducting electromagnets in MRI machines. There the current is high enough that the force is noticeable, and the coil of wire has to be reinforced so that it can hold its shape.

Source: UCSB ScienceLine

As for power lines they are placed quite far apart from each other hence the net magnetic force gets reduced.

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    $\begingroup$ The question was regarding transmission power lines. $\endgroup$
    – Sam
    Feb 23, 2020 at 5:28
  • $\begingroup$ Those are placed quite far from each other hence it reduces the magnetic force in them $\endgroup$
    – Abhirup Adhikary
    Feb 23, 2020 at 5:31

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