# Lorentz Force questions

#### ben sorenson

Joined Feb 28, 2022
181

Hello, I'm trying to get a better understanding of the Lorentz force. I get the fundamentals I think but the law states the force is applied to --- charged partials --- and I've seen the water whirlpool effect with magnets. In this case the charged partial is the ions in the water or something? So the water spins because is particals are charged.

My next question is, what is considered a "charged partical"?

Is a charged partical only a partical within a conductive medium,does the force only apply to materials that are conductive or does the force apply to all materials?

If the force only applies to materials that are conductive then...

What would the significance be if the Lorentz force could be applied and seen on a material / object that is non conductive?

For example what would it mean if instead of water circulation in a cup showing off the Lorentz force by the em field if let's say the cup was filled with rocks and the rocks moved in a circular motion.

Is that even possible? If it was what would that mean? Would that require more energy or less energy than seeing it with the water?

#### Wendy

Joined Mar 24, 2008
23,475
I might be mistaken but I believe whirlpools are caused from the Coriolis force, caused from the spin of the earth. The direction of the spin is dependent on what side of the equator. If you are south of the equator the whirlpool spins the other way than the north does.

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#### ZCochran98

Joined Jul 24, 2018
305
I might be mistaken but I believe whirlpools are caused from the Coriolis force, caused from the spin of the earth. The direction of the spin is dependent on what side of the equator. If you are south of the equator the whirlpool spins the other way than the north does.
That's not actually generally true. The Coriolis effect causes rotations in atmosphere, which DO generally follow that rule-of-thumb, but you can get a whirlpool in either direction in the equator, depending on the initial current flow. In the case of oceanic ones? Those will follow ocean currents (due to the Coriolis effect), and also follow that rule-of-thumb. However, water going down a drain is not dictated by the Coriolis effect, due to the tiny effect locally the Earth's rotation will have. It's a much more prevalent effect at larger scales.

In the case of the water flowing due to electricity, that's partially due to ionization, partially due to the polarity of water. The flow of water would be due to having a large enough electric field to repel (or attract) the water molecules (as they're slightly polar). If the flow is circular, it's because the way the magnetic field is set up.

As far as the Lorentz Force is concerned, a "charged particle," for most purposes, is an electron, though it could be anything with charge. Recalling the equation:

$\textbf{F} = q\left(\textbf{E} + \textbf{v}\times\textbf{B}\right)$

If anything has any kind of charge, then an electric field will apply a force to it (including the rocks!). If the charges also have a velocity, then in the presence of a magnetic field, they'll experience a force there, too! However, the force due to the magnetic field will be perpendicular to the present direction of the velocity and the magnetic field, which can cause rotations (like a whirlpool). So, for instance, in the case of the water, a strong electric field can get the water moving, but then a magnetic field pointing straight into (or out of) the pool can get it to start circulating once the water is moving.

Anything that has a net charge can experience this, though the force may be exceptionally minuscule. You could, per your example, get a bunch of rocks to circulate, too, but you'd need a really, really large set of fields to do this (so, yes: a lot higher electromagnetic potential energy), and rocks with a net charge.

In regards to your question about conductive vs non-conductive materials, that'll determine the effect. In the case of a charged non-conductive material? The entire nonconductor will be the "unit of charge," as the charges in the material are not free to move. In the case of a conductor, the charges in the material are free to move, so they are the "unit of charge." In this case, you end up with circulation currents in the material that will create a magnetic field to oppose the original one (take a look at magnetic braking).

Tl;dr: "charged particles" can mean anything. It's basically the smallest unit of "free charges" allowed, whether it's a large insulating object with an excess of electrons (or lack of them), or it's an electron in a metal. What ends up circulating or moving depends on the result. Deionized and distilled water is nonconductive, so the smallest unit of "free charge" is the water molecule itself (it doesn't properly have a net charge; just separates its equal charges enough to give an electric dipole), so the water will move. Copper contains a ton of electrons in conduction, so the smallest unit of free charge there is the electron, so the electrons will move.

Hope that clears things up a bit!

#### WBahn

Joined Mar 31, 2012
30,294
I might be mistaken but I believe whirlpools are caused from the Coriolis force, caused from the spin of the earth. The direction of the spin is dependent on what side of the equator. If you are south of the equator the whirlpool spins the other way than the north does.
This is, in general, not true. The Coriolis force only has enough of an effect to force this behavior when you get to hurricane-scale rotations. Even tornados can spin the "wrong way" -- about five percent of them do. But this strong preference for spinning the "right" direction is not due to the Coriolis force acting on things the scale of the tornado, but rather acting on the overall weather pattern on the scale of the associated low pressure system (which is generally hurricane-scale in dimensions). Thus the air movements that eventually coalesce to make the tornado are already moving with a strong bias in the "correct" direction and, despite this, about one in twenty still experience local random movements sufficient to get them going the "wrong" way.

On the scale of whirlpools in oceans, lakes, bays and such, the direction of rotation is due to the specific features that give rise to the whirlpool and can be in either direction, but in places where a whirlpool appears regularly, the direction is almost always the same because the features are the same. About the only thing that would affect that would be if one whirlpool appears in a rising tide and the another in a falling tide, but those are really two different whirlpools, each with a stable direction.

On the human-size scale, like sinks and toilets, the direction is due to the bias when the whirlpool is established. In sinks it tends to be random, in toilets the holes under the rim are usually angled specifically to set up a strong whirlpool and can be in either direction.

#### ben sorenson

Joined Feb 28, 2022
181
That's not actually generally true. The Coriolis effect causes rotations in atmosphere, which DO generally follow that rule-of-thumb, but you can get a whirlpool in either direction in the equator, depending on the initial current flow. In the case of oceanic ones? Those will follow ocean currents (due to the Coriolis effect), and also follow that rule-of-thumb. However, water going down a drain is not dictated by the Coriolis effect, due to the tiny effect locally the Earth's rotation will have. It's a much more prevalent effect at larger scales.

In the case of the water flowing due to electricity, that's partially due to ionization, partially due to the polarity of water. The flow of water would be due to having a large enough electric field to repel (or attract) the water molecules (as they're slightly polar). If the flow is circular, it's because the way the magnetic field is set up.

As far as the Lorentz Force is concerned, a "charged particle," for most purposes, is an electron, though it could be anything with charge. Recalling the equation:

$\textbf{F} = q\left(\textbf{E} + \textbf{v}\times\textbf{B}\right)$

If anything has any kind of charge, then an electric field will apply a force to it (including the rocks!). If the charges also have a velocity, then in the presence of a magnetic field, they'll experience a force there, too! However, the force due to the magnetic field will be perpendicular to the present direction of the velocity and the magnetic field, which can cause rotations (like a whirlpool). So, for instance, in the case of the water, a strong electric field can get the water moving, but then a magnetic field pointing straight into (or out of) the pool can get it to start circulating once the water is moving.

Anything that has a net charge can experience this, though the force may be exceptionally minuscule. You could, per your example, get a bunch of rocks to circulate, too, but you'd need a really, really large set of fields to do this (so, yes: a lot higher electromagnetic potential energy), and rocks with a net charge.

In regards to your question about conductive vs non-conductive materials, that'll determine the effect. In the case of a charged non-conductive material? The entire nonconductor will be the "unit of charge," as the charges in the material are not free to move. In the case of a conductor, the charges in the material are free to move, so they are the "unit of charge." In this case, you end up with circulation currents in the material that will create a magnetic field to oppose the original one (take a look at magnetic braking).

Tl;dr: "charged particles" can mean anything. It's basically the smallest unit of "free charges" allowed, whether it's a large insulating object with an excess of electrons (or lack of them), or it's an electron in a metal. What ends up circulating or moving depends on the result. Deionized and distilled water is nonconductive, so the smallest unit of "free charge" is the water molecule itself (it doesn't properly have a net charge; just separates its equal charges enough to give an electric dipole), so the water will move. Copper contains a ton of electrons in conduction, so the smallest unit of free charge there is the electron, so the electrons will move.

Hope that clears things up a bit!
Thak you so much for your reply! How big of a field you suppose would be needed for the rocks to circulate? Just curious

#### ZCochran98

Joined Jul 24, 2018
305
Depends on the rocks and the material, but considering how little charge they probably accumulate, quite a big field. Let's assume we have a small (~1cm diameter) sphere of silica (a very common mineral), which has, very roughly, about -1 mC per square meter of surface (as charges in silica tend to collect near the surfaces). So that puts us at a net charge of $$4\pi\left(\frac{0.01}{2}\right)^2\cdot\left(-1\right) = 0.00031$$ mC of charge, with a total mass (of one sphere of silica) of $$\frac{4}{3}\pi\left(\frac{1}{2}\right)^3\cdot 0.00265 = 0.0014$$ kg. To get the rock moving at any appreciable velocity (let's say 1 sphere length per second, or 1 cm/s) in 1 second (so 0.01 m/s/s), we'll need to have a base electric field to get it started of $$E = \frac{F}{q} = \frac{ma}{q} = \frac{-0.0014\cdot 0.01}{0.00031\times 10^{-3}} = -45$$ V/m, which isn't really all that much (this is assuming, of course, that there really is that much free charge on the surface of the silica sphere). Then, if it's moving at 1 cm/s along the direction of the electric field at that instant, to get it to move in a radius of, say, 10 cm (as an arbitrary example), we need to figure out first, what force that requires, and second, the magnetic field required. From centripetal acceleration:

$F = \frac{mv^2}{r}$

We can get our required force. We can go straight to magnetic field magnitude (assuming a constant velocity! This means the electric field needs adjusted in magnitude to keep tangential velocity constant):

$F = \frac{mv^2}{r} = qvB \rightarrow B = \frac{mv}{qr} = \frac{0.0014\cdot 0.01}{0.00031\times 10^{-3}\cdot 0.1} \approx 452$

So you'd need a 452 T field. That's REALLY big. For perspective, it takes 17 T to levitate a frog due to the paramagnetic properties of blood and water.

Doing some sanity checks, we can check the velocity number given the potential energy the electric field will provide for the rock when it moves over the span of distance required to get it to 1 cm/s ($$x = \frac{v_f^2}{2a} = \frac{0.01^2}{0.02} = 0.5$$ cm). $$U = Eqx \rightarrow \frac{1}{2}mv^2 = Eqx \rightarrow v = \sqrt{\frac{2Eqx}{m}} = \sqrt{\frac{2\cdot 45\cdot 0.00031\times 10^{-3}\cdot 0.005}{0.0014}} = 0.01$$ m/s, or 1 cm/s (the math checks out!). Then, for the magnetic field, we take the magnetic moment-based potential energy and the rotational energy:

$U = \mu B = IAB = \pi r^2 B \frac{dq}{dt} = \frac{1}{2} m r^2 \omega^2$

Here, $$\omega$$ is the angular frequency, or $$\omega = \frac{v}{r}$$, and $$\mu$$ is the magnetic dipole moment of a moving charge (the current it exhibits multiplied by the area it circulates over). Current is hard to define in this particular case, but we can imagine it as the amount of charge that passes by a point per second. That can be, roughly-speaking, $$\frac{dq}{dt} = \frac{q\omega}{2\pi}$$. So, putting it all together:

$\pi r^2 B q \frac{v}{2\pi r} = \frac{1}{2} m r^2 \frac{v^2}{r^2} \rightarrow B = \frac{mv}{qr}$

Which is exactly the same equation (the "cyclotron equation") we got before! That means (barring any calculator errors) that the magnetic field we calculated is consistent for the tangential velocity we wanted, using both the Lorentz law and magnetic potential energy methods. We could have done this pure equation-based method for the electric field as well, but that wouldn't have verified any specific numbers; just that the equations work out to be the same.

Tl;dr: to get a 1 cm sphere of silica accelerating at 1 cm/s/s initially until it has a velocity of 1 cm/s, and then to get it moving in a 10 cm radius circle, we would need an electric field of 45 V/m and a magnetic field of 452 T (or 10x stronger than the strongest man-made magnetic field and 26.6x stronger than the field required to levitate a frog). All of this ignoring friction, impurities, and other external factors.

Edit: I should point out I'm being VERY sloppy with the signs here, but that's ONLY because I'm working with magnitudes, overall. To get directional information, you'd need to properly handle the signs (this also includes the fact that, technically, the potential energy in a magnetic field equation is missing a negative sign, as the magnetic field only has any form of energy when the objects have some kind of motion. Or you're dealing with point particles with quantum spin, in which case $$\mu$$ is related to the dipole moment of an electron, which is, in turn, related to spin and some gyroscopic constant).

Edit 2: The magnetic field would need to be perpendicular to the electric field and the direction of initial travel of the silica sphere. So, if the sphere were moving along the x-axis (along with the direction of the electric field), then the magnetic field would have to be on the z-axis (for a circle to be traced out in the XY-plane), or the y-axis (for the circle to be traced out in the XZ-plane).

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#### ben sorenson

Joined Feb 28, 2022
181
Depends on the rocks and the material, but considering how little charge they probably accumulate, quite a big field. Let's assume we have a small (~1cm diameter) sphere of silica (a very common mineral), which has, very roughly, about -1 mC per square meter of surface (as charges in silica tend to collect near the surfaces). So that puts us at a net charge of $$4\pi\left(\frac{0.01}{2}\right)^2\cdot\left(-1\right) = 0.00031$$ mC of charge, with a total mass (of one sphere of silica) of $$\frac{4}{3}\pi\left(\frac{1}{2}\right)^3\cdot 0.00265 = 0.0014$$ kg. To get the rock moving at any appreciable velocity (let's say 1 sphere length per second, or 1 cm/s) in 1 second (so 0.01 m/s/s), we'll need to have a base electric field to get it started of $$E = \frac{F}{q} = \frac{ma}{q} = \frac{-0.0014\cdot 0.01}{0.00031\times 10^{-3}} = -45$$ V/m, which isn't really all that much (this is assuming, of course, that there really is that much free charge on the surface of the silica sphere). Then, if it's moving at 1 cm/s along the direction of the electric field at that instant, to get it to move in a radius of, say, 10 cm (as an arbitrary example), we need to figure out first, what force that requires, and second, the magnetic field required. From centripetal acceleration:

$F = \frac{mv^2}{r}$

We can get our required force. We can go straight to magnetic field magnitude (assuming a constant velocity! This means the electric field needs adjusted in magnitude to keep tangential velocity constant):

$F = \frac{mv^2}{r} = qvB \rightarrow B = \frac{mv}{qr} = \frac{0.0014\cdot 0.01}{0.00031\times 10^{-3}\cdot 0.1} \approx 452$

So you'd need a 452 T field. That's REALLY big. For perspective, it takes 17 T to levitate a frog due to the paramagnetic properties of blood and water.

Doing some sanity checks, we can check the velocity number given the potential energy the electric field will provide for the rock when it moves over the span of distance required to get it to 1 cm/s ($$x = \frac{v_f^2}{2a} = \frac{0.01^2}{0.02} = 0.5$$ cm). $$U = Eqx \rightarrow \frac{1}{2}mv^2 = Eqx \rightarrow v = \sqrt{\frac{2Eqx}{m}} = \sqrt{\frac{2\cdot 45\cdot 0.00031\times 10^{-3}\cdot 0.005}{0.0014}} = 0.01$$ m/s, or 1 cm/s (the math checks out!). Then, for the magnetic field, we take the magnetic moment-based potential energy and the rotational energy:

$U = \mu B = IAB = \pi r^2 B \frac{dq}{dt} = \frac{1}{2} m r^2 \omega^2$

Here, $$\omega$$ is the angular frequency, or $$\omega = \frac{v}{r}$$, and $$\mu$$ is the magnetic dipole moment of a moving charge (the current it exhibits multiplied by the area it circulates over). Current is hard to define in this particular case, but we can imagine it as the amount of charge that passes by a point per second. That can be, roughly-speaking, $$\frac{dq}{dt} = \frac{q\omega}{2\pi}$$. So, putting it all together:

$\pi r^2 B q \frac{v}{2\pi r} = \frac{1}{2} m r^2 \frac{v^2}{r^2} \rightarrow B = \frac{mv}{qr}$

Which is exactly the same equation (the "cyclotron equation") we got before! That means (barring any calculator errors) that the magnetic field we calculated is consistent for the tangential velocity we wanted, using both the Lorentz law and magnetic potential energy methods. We could have done this pure equation-based method for the electric field as well, but that wouldn't have verified any specific numbers; just that the equations work out to be the same.

Tl;dr: to get a 1 cm sphere of silica accelerating at 1 cm/s/s initially until it has a velocity of 1 cm/s, and then to get it moving in a 10 cm radius circle, we would need an electric field of 45 V/m and a magnetic field of 452 T (or 10x stronger than the strongest man-made magnetic field and 26.6x stronger than the field required to levitate a frog). All of this ignoring friction, impurities, and other external factors.

Edit: I should point out I'm being VERY sloppy with the signs here, but that's ONLY because I'm working with magnitudes, overall. To get directional information, you'd need to properly handle the signs (this also includes the fact that, technically, the potential energy in a magnetic field equation is missing a negative sign, as the magnetic field only has any form of energy when the objects have some kind of motion. Or you're dealing with point particles with quantum spin, in which case $$\mu$$ is related to the dipole moment of an electron, which is, in turn, related to spin and some gyroscopic constant).

Edit 2: The magnetic field would need to be perpendicular to the electric field and the direction of initial travel of the silica sphere. So, if the sphere were moving along the x-axis (along with the direction of the electric field), then the magnetic field would have to be on the z-axis (for a circle to be traced out in the XY-plane), or the y-axis (for the circle to be traced out in the XZ-plane).
Like this?

#### ZCochran98

Joined Jul 24, 2018
305
Possibly. That might be silica or a similar material, though it is probably spinning under some other effect (less of the Lorentz force and probably a combination of other things - a little hard to tell what exactly is happening there). But yeah: if that's silica, then something like that.

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#### ben sorenson

Joined Feb 28, 2022
181
Do you think it's spinning from some other affect because that size of magnetic field doesn't currently exist?

#### ZCochran98

Joined Jul 24, 2018
305
Correct, and other effects can cause things to spin; I just can't quite tell what's happening in that video well enough to give an explanation. Furthermore, the Lorentz force would not cause something to spin on its axis, but instead rotate around a fixed point (unless the object were large enough and had a SIGNIFICANT buildup of charge in one spot on the surface, rather than be distributed relatively-evenly across the entire surface).

#### ben sorenson

Joined Feb 28, 2022
181
Correct, and other effects can cause things to spin; I just can't quite tell what's happening in that video well enough to give an explanation. Furthermore, the Lorentz force would not cause something to spin on its axis, but instead rotate around a fixed point (unless the object were large enough and had a SIGNIFICANT buildup of charge in one spot on the surface, rather than be distributed relatively-evenly across the entire surface).
Here is another view, a little better. You may have to zoom in with your screen. There is something that happens like a burst of electricity about half way through, the electricity turns to a pink purple and the rock starts spinning in another direction @ (1:12) Any idea what that could be?

#### ZCochran98

Joined Jul 24, 2018
305
Without knowing the exact setup used, I can only hypothesize. From this and the previous video, it appears, possibly, the sphere is being ionized and then undergoing some kind of static discharge. This discharge might cause it to "jump" a bit and spin a bit. Do this fast enough with strong enough discharge at just the right spot, it might be able to spin. I don't think the wire coils he has in there are actually doing anything; they appear to be holding the sphere in place, and that's about it.

#### ben sorenson

Joined Feb 28, 2022
181
Without knowing the exact setup used, I can only hypothesize. From this and the previous video, it appears, possibly, the sphere is being ionized and then undergoing some kind of static discharge. This discharge might cause it to "jump" a bit and spin a bit. Do this fast enough with strong enough discharge at just the right spot, it might be able to spin. I don't think the wire coils he has in there are actually doing anything; they appear to be holding the sphere in place, and that's about it.
If the rock or crystal that's in there is getting ionized, wouldn't that take voltage of a mev magnitude? And if it's being truly ionized would that be considered along the lines of a nuclear reaction of some sort?

#### ZCochran98

Joined Jul 24, 2018
305
"Ionized" wasn't a good choice of words on my part; it's more that an excess of electrons built up at one spot on the sphere and then pulled from the surface through static discharge, which at that scale would be ~10-50kV (like a taser). And no: ionization does NOT mean, in any sense, nuclear reactions. Nuclear reactions require actual things to happen to the atomic nuclei.

#### MrSalts

Joined Apr 2, 2020
2,767

#### Janis59

Joined Aug 21, 2017
1,863
Charged particle concept: if metall - then it is less or more similar to spherical capacitor, charged ball. Where physically stays thius charge - on the outer surface according Faraday cage principle: all existing charge is swept off from inside surface and drift to outside surface. Other case is insulator. All insulators charge by surface uniform charge. Thus, the result in both cases are accurately identical.