[hamdani yusuf (OP)]

We can consider this experiment as a variation of Marinov motor. In the original version, the magnet is in toroidal form, which makes the magnetic field around it is close to 0. In this video, the conductive liquid is used instead of metal ring which act as rotor.
Which part of Maxwell's equations applies here? Does it have anything to do with Lorentz' force? Does it involve another electromagnetic interaction? 

[alancalverd]

Fleming's Left-hand Motor Rule. The effective field in this case is vertical i.e. perpendicular to the plane of the liquid.

[RD]

If one of the electrodes was dangling it would be a Faraday motor ...

Further reading ... https://wikipedia.org/wiki/Magnetohydrodynamic_converter

[hamdani yusuf (OP)]

The effective field in this case is vertical i.e. perpendicular to the plane of the liquid.

What makes the effective field different than measured magnetic field?
In the original setup, the magnet being used is a toroid. It means the B field around it is close to 0.

[alancalverd]

The lines of force run from N to S both vertically and horizontally. If there were no field, there would be no movement.

[hamdani yusuf (OP)]

The lines of force run from N to S both vertically and horizontally. If there were no field, there would be no movement.

How do the lines of force distributed? It should explain the observation that the direction of liquid movement is counter clockwise when the electrodes are located outside of the liquid ring. But it reverses when they are placed inside of liquid ring.

[alancalverd]

There has to be some initial asymmetry to determine the direction of the current flow: if the electrodes and magnetic field were perfectly symmetrical the current would flow equally in both directions and there would be no movement! Once the liquid flow has started, that pretty well determines the current direction depending on whether the positive or negative ions are more mobile.

Experiments with bath water (does it spin the other way south of the equator?) have shown that micro-flow persists for hours after the bath is filled. In this case if the bulk of the conductive liquid is flowing, say, clockwise, that will persist when the electrodes are removed, but turbulence at the surfaces may produce local countercurrent eddies that will start the flow in the opposite direction when you move the electrodes.

Some old electric clocks had symmetric synchronous motors, and in the days when we had frequent power outages I recall my grandmother's clock sometimes stationary and often running backwards when the power was restored!

[hamdani yusuf (OP)]

There has to be some initial asymmetry to determine the direction of the current flow: if the electrodes and magnetic field were perfectly symmetrical the current would flow equally in both directions and there would be no movement! Once the liquid flow has started, that pretty well determines the current direction depending on whether the positive or negative ions are more mobile.

Experiments with bath water (does it spin the other way south of the equator?) have shown that micro-flow persists for hours after the bath is filled. In this case if the bulk of the conductive liquid is flowing, say, clockwise, that will persist when the electrodes are removed, but turbulence at the surfaces may produce local countercurrent eddies that will start the flow in the opposite direction when you move the electrodes.

Some old electric clocks had symmetric synchronous motors, and in the days when we had frequent power outages I recall my grandmother's clock sometimes stationary and often running backwards when the power was restored!

The experiment shows that the effect is consistent by repeatedly switching direction, thus it's not just an artefact.
The question would be, what kind of asymmetry could explain the observed result?

[alancalverd]

Two separate questions.

First, there must be an initial asymmetry in order for there to be any movement. Your diagram shows "i"  in both directions, so no gross motion is possible without an asymmetric trigger.

Second, once movement has been established, the inevitable turbulence (you can see it in the video) provides the trigger to reverse the flow.

Or it's magic.

[hamdani yusuf (OP)]

The diagram in #3 is the original setup. The brush connected to the ring rotor on the outside only.
The video shows some modifications. It uses liquid conductor. The electrodes can be placed anywhere on the liquid ring.
The asymmetry seems to come from the radial electric current in the toroid plane.
The flow direction is consistently determined by the position of the electrodes. No turbulence is required.

[alancalverd]

If the system is completely symmetrical, nothing will move. It is the principle used in residual current magnetic circuit breakers.

[hamdani yusuf (OP)]

If the system is completely symmetrical, nothing will move. It is the principle used in residual current magnetic circuit breakers.

The problem is, the B field around the toroid supposed to be 0. But still we find that some electromagnetic force is generated.

[alancalverd]

Supposed by whom? If you take the magnet away, you certainly will have zero field. Does the motor work then? I suspect not, so B_ext≠0.

[hamdani yusuf (OP)]

The absence of circumferential current [4] (the path of circumferential current is indicated by the red arrow in figure 3 of this section) and the axially symmetric layout of the conductors and magnetic materials [4][5][6] are sufficient conditions for total internal confinement of the B field. (Some authors prefer to use the H field). Because of the symmetry, the lines of B flux must form circles of constant intensity centered on the axis of symmetry. The only lines of B flux that encircle any current are those that are inside the toroidal winding. Therefore, from Ampere's circuital law, the intensity of the B field must be zero outside the windings.

https://en.wikipedia.org/wiki/Toroidal_inductors_and_transformers#Sufficient_conditions_for_total_internal_confinement_of_the_B_field

[alancalverd]

I say again, if B= 0 it will work without the magnet.

[Bored chemist]

I say again, if B= 0 it will work without the magnet.

He's not wrong.

[hamdani yusuf (OP)]

I say again, if B= 0 it will work without the magnet.

Do you know about Aharonov-Bohm Effect? Or magnetic vector potential?
Have you watched this video?

Scientists have often thought that magnetic (and electric) fields are fundamental quantities that relate to real, physical, observable things in the universe. And they are. But, it may be possible that their potentials are even more fundamental! #quantumphysics #quantummechanics #aharonovbohm  #electromagnetism #magneticfields #electricfields

Hey everyone, in this video I wanted to discuss how a quantity initially created purely for mathematical convenience, ends up being a really important fundamental quantity in the study of quantum mechanics.

Magnetic fields (B) are used to describe how magnets interact with each other - both the creator of the field, and any magnet placed within the field. And these fields are thought to be fundamental quantities, neatly describing the behaviour of all magnetic objects. However, sometimes magnetic fields are not mathematically simple to deal with.

To overcome this issue, physicists made use of a neat math trick. They took an identity that states that the divergence of the curl of any vector must be zero, as well as the Maxwell equation that states that the divergence of any magnetic field must always be zero ( 

 ? Let There Be Light: Maxwell's Equatio...  ) to define a "magnetic vector potential" (A). The relationship is that a magnetic field is equal to the curl of its vector potential.

Now vector potentials are often easier to work with mathematically, but they aren't uniquely defined ("gauge invariance"). If we have a certain B-field, this can be described by multiple related A-fields. But when given an A-field, we can uniquely find the corresponding B-field. This is important later.

When studying quantum mechanics, it turns out that the A-field can have a real, measurable impact on a system, despite only being considered a mathematical convenience. Importantly, this measurable impact has nothing to do with the corresponding B-field! This is because in a region of space where B is zero, but A is not zero, we can find the wave function of an electron being changed. Specifically, the phase of the wave function changes, and this can be measured using a particular type of double-slit experiment. This effect is known as the Aharonov-Bohm Effect.

In other words, we find that the magnetic vector potential can have a real-world impact WITHOUT any influence from its corresponding magnetic field. The Aharonov-Bohm effect is telling us that electric and magnetic fields are not the fundamental quantities that we initially thought, and their potentials are the fundamental quantities! This despite potentials only being created for mathematical convenience!

Caveat to the Aharonov-Bohm effect: It may be possible to describe the effect by purely dealing with the magnetic field and not the vector potential, but this would involve having to give up the idea of locality - we would need nonlocal fields! (https://en.wikipedia.org/wiki/Princip...)

Timestamps:
0:00 - Magnetic Field Lines: Vectors for Magnetic Interactions
1:46 - Magnetic Fields vs Mathematical Convenience
2:17 - A Neat Trick for Defining Magnetic Vector Potential
4:00 - Sponsor Chat: Thanks to Skillshare, Check Out a Free Trial Below!
5:00 - Gauge Invariance, Uniquely Defining the Vector Potential
6:08 - B Fields are the Real Fundamental Quantity... Right?!
6:45 - Passing an Electron Near a Solenoid (Coil of Wire)
7:56 - Phase and the Aharonov-Bohm Effect
9:40 - Final Thoughts