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I am a junior electrical engineering student, recently we were learning about the circuit breakers and professor showed us a video of an electrical arc which can be seen in the picture (Sorry for the quality). I wondered "if electrical arc is actually the electrons that are moving" why electrical arc didn't move in straight line but chose to rise and connect. I asked the lecturer about this but what I heard was just some gibberish. Then I thought about it and did some research but couldn't really find something directly about this. I believe it is caused by the Lorentz forces and also the rising of the warm air. But if warm air rises it should reduce the pressure of the air in the top side. Which will increase the distance between the particles in air and make it harder for air to ionize, right? Can you explain it to me or give me your thoughts about it?

enter image description here

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    \$\begingroup\$ You don't need thoughts. It's not as though the topic hasn't been studied to death. Just glancing over at my library, I see three of the five books I have on just this topic alone: "The Art and Science of Lightning Protection" by Martin Uman; "Lightning Physics and Lightning Protection" by Bazelyan & Raizer; and this one on quantitative physical theory for plamas, "Principles of Plasma Discharges and Materials Processing" by Lieberman & Lichtenberg. The first two are filled with experimental data and experience. The last is pure plasma physics theory. But just get a good book. \$\endgroup\$
    – periblepsis
    Commented May 20 at 18:55

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When the potential between the two conductors reaches sufficient voltage, it causes a breakdown in the air - ionising the air into a hot plasma between the two conductors. It is this plasma through which a sustained current can flow because it is significantly lower resistance than the surrounding air.

Because the plasma channel is hotter than the surrounding air, it will start to rise - think convection currents. Remember though it is this plasma that is conducting the current and emitting light, and so as the plasma rises, so will the arc.

Up to a point, the plasma is still such a low resistance compared to the surrounding air and still ionised, the extra distance of this path doesn't initially disrupt the current flow. At some point there is not enough thermal energy or electric potential to keep the arc ionised and the plasma begins to both disperse (mix with the surrounding air) and recombine (ions return to ground state).

If there is still enough potential between the conductors a new arc will form and the process repeats. A great example of this is a Jacobs ladder (travelling arc). In this example the Lorentz force is not actually the driving factor of the arc rising - for example this answer links to a video of an upside down Jacobs Ladder where the arc no longer moves along the ladder as would be expected if the magnetic forces were dominant.

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  • \$\begingroup\$ The air that heats up and rises is actually ionized air. So another heated air does not merge with the ionized air above. Instead the ionized part heats up and rises. Do I understand you correctly? \$\endgroup\$
    – kaan
    Commented May 20 at 17:52
  • \$\begingroup\$ There is something else, that is, the discharge, having a certain energy, it is transformed partly into heat and sound energy, another fraction is transformed into electromagnetic energy radiated into space at a frequency around 100MHz, another part is transformed into light energy and finally a small fraction also into X-rays. \$\endgroup\$
    – Franc
    Commented May 20 at 18:09
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    \$\begingroup\$ @kaan pretty much. It takes quite a while to transfer heat from the arc into the surrounding air, so initially it is the plasma that is rising. Convection currents will be formed causing motion in the surrounding air (likely chaotic hence the weird shape of the arc). Everything will ultimately mix back together which is why the arcs tend to get quite "hazy" for lack of a better term as they move upwards. \$\endgroup\$
    – Tom Carpenter
    Commented May 20 at 18:12
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The electrical arc is heated up quite a bit compared to the atmospheric air. Like a hot air balloon, the arc is at lower density than ambient air so the arc rises.

A large, high energy arc like you show in the photo will have a lot of heat, and thus a lot of swirling convection which stirs up the plasma into the random-looking shape you see. A smaller arc (like a Jacob’s ladder) won’t have as much heat or space so will tend to rise more regularly, without the swirling.

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  • \$\begingroup\$ Do you think Lorentz forces also effect arc to rise or not ? \$\endgroup\$
    – kaan
    Commented May 20 at 17:53
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But if warm air rises it should reduce the pressure of the air in the top side. Which will increase the distance between the particals in air and make it harder for air to ionize, right ?

Plasma also has resistance which is small, but you can get heating in plasma from a large current. The plasma is heated and the arc sustains the plasma, this process continues until the plasma gets pinched by air and the arc is extinguished. So it's really the self heating of the plasma that keeps the arc going, the heated air rises and also the lorentz forces push it upwards.

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