# The way Lenz force can accelerate a magnet

• cala
In summary, the Faraday and Lenz laws state that the EMF opposes flux variation, nothing more, nothing less. If you manage to get these two concepts "out of phase" you can't say that opposing one is opposing the other.

#### cala

Hello.

I have problems with the Faraday and Lenz laws. Not problems with their definitions (they are OK), but with the usual assumptions and relation with conservation of energy:

The definition of these two laws states:

- Faraday law: The induced electromotive force or EMF in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit.

- Lenz law: The induced emf and the change in flux have opposite signs.

OK. Also, we know 3 ways of changing flux on a closed loop: moving a magnetic field over the closed loop, changing the field intensity, or changing the closed loop surface.

My problems come with the first method of magnetic induction: moving a magnet over a coil.

Usually, we say that the EMF opposition on the coil opposes the movement of the magnet, because (usually) flux increases when poles come closer to the coil, and decrease when they leave.

But the Faraday/Lenz law has nothing to do with "movement". They state that the EMF opposes flux variation, nothing more, nothing less. (... And, of course, nothing about movement here)

Usually we say that opposition to flux change is the same as opposition to movement, because the magnetic flux is always "linked" to magnet poles... That is right.

But there is a method to have the flux SEEN BY COILS "out of phase" respect magnet movement (flux is really linked to magnet poles, but not linked to how it traverses the coil surfaces). If we get the flux "out of phase" respect to movement, the Lenz force will oppose to the flux variation, as usual... but no longer to the movement! In this case, the Lenz force could in fact accelerate the magnet movement instead opposing it!

The way to get flux increasing when the magnet poles are leaving, and get the flux decreasing when a magnet pole is approaching is... just placing the coil surfaces perpendicular to magnet pole surface while the magnet rotates.

For example, there is an illustrative experiment to show the classic Lenz force opposition to movement, that consist in throwing a magnet through an aluminium or copper tube. As the magnet go down the tube due to gravity, the flux changes in front and behind the magnet in such a way that the Lenz force opposes the flux change... and also the movement. The final effect is that the magnet slows down when going through the tube.

BUT... What about a magnet rotating inside the hole of an aluminium or copper toroid? (just like the hands in a clock)

You can see that this way, the flux change on the toroid sections is "out of phase" respect the magnet rotation. The increase of the flux is not "attached" to a magnet pole approaching (in fact, the increase of the flux happens when the poles leave that section!) and the decrease on the flux happens when magnet poles approach to a given section of the toroid!

In such a case, the Lenz force will do what is stated to do: oppose the flux change... but as the flux is "out of phase" from the magnet pole movement... the Lenz force will accelerate the magnet!

I know that Lenz law is always seen related to conservation of energy in electric systems, but you can see that there is something wrong in the usual assumption of "opposition to flux change" being equal to "opposition to movement". If we manage to get these two concepts "out of phase" we can't say that opposing one is opposing the other.

... What do you think?

I post a drawing of the two experiments: the magnet on the tube and inside the toroid ring.

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• lenz.JPG
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I post another drawing, with parallel coil surface orientation, and perpendicular coil surface orientation, and their different effects on magnetic induction when magnet rotates. (Coil surface normal for the graphics is indicated on the drawing by a line)

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• magnet-coil rotation.JPG
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I've posted how a magnet in movement can be "out of phase" respect the flux change it creates on a coil surface.

Usually we use the magnet flux lines that comes out from the magnet poles, but a magnet is not a source nor a sink of magnetism, it is both at the same time (a dipole).

A magnet is in fact a closed system from the point of view of magnetic flux.

Imagine you could surround a magnet and all the space around it with a coil surface. You'll have no flux change, independently of the rotation of the magnet, because you'll be cutting the lines that comes out from the magnet... and the lines "going back" to the magnet that are sitting on the space around the magnet.

What I want to say is that every "real" magnet has "virtual" magnets on the space surrounding them, with opposite polarity. We can move the real magnet, but cut the lines of the virtual magnets with a coil surface, then get magnetic induction from the flux change caused by the virtual magnets, but the Lenz force acting on the real magnet...

I post a drawing that depicts the "virtual" magnet regions around a bar magnet.

Still have to think about the final explanation on this paradox of having coils generating useful electric voltage and current, and at the same time accelerating the magnet rotor...

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• virtual magnets.JPG
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Hi. I post the way we can get the "virtual" magnet regions trapped into a ring of iron, to "trap" all the flux and make it available for coil surfaces. Also, I post an animation of the magnetic field that appears on the coils when moving the magnet. The Lenz force appears to be accelerating the magnet instead opposing it, as the coils feels the movement of the "virtual" magnets, then reacts to that flux change, but the Lenz Force really have effect on the "real" magnet (90º out of phase respect flux change seen by the coils).

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• virtual magnets 2.JPG
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• rotor.gif
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The ring of iron will react to the movement of the magnet regions. If the iron becomes polarized by the reaction of the movement of the magnet, seems to me that the real effect of the polarisation of the iron will actually be to deaccelerate the magnet due to the lenz effect and because the ring iron is only temporarily magnetised and the effect caused on the magnet is of opposition and deacceleration. That's my thought.

I squared R losses and heating need to be considered.

One of the classic mistakes that is often made when studying electrodynamics is to create a situation that is so complicated that it defies simple analysis. Or at least makes it difficult.
From that position it becomes easy to convince yourself that black is white.

If you simplify your toroid by taking a short sector, you will see that in essence it is no different than a single loop coil with the magnet pole rotating past. You can simplify further, by assuming a large radius and having the magnet pole simply pass by, moving parallel to the axis of the coil.

Now that you have a simple model of the situation, if you apply the appropriate rules, you will see that the induced current generates a field to oppose the motion.
In fact it's exactly the same as your solenoid model, with the magnet passing on the outside instead of the inside.
(NB. current - not emf - emf does not generate a field, current does)

## 1. How does the Lenz force work?

The Lenz force is a phenomenon in electromagnetism that occurs when a changing magnetic field induces a current in a conductor. This induced current creates its own magnetic field that opposes the original changing magnetic field. This opposing force is known as the Lenz force and it is the reason why a magnet can be accelerated when placed in a changing magnetic field.

## 2. What is the relationship between the Lenz force and Newton's third law?

According to Newton's third law, for every action, there is an equal and opposite reaction. In the case of the Lenz force, the action is the changing magnetic field and the reaction is the induced current, which creates an opposing force. This is in line with Newton's third law as the two forces are equal and opposite.

## 3. Can the Lenz force accelerate any type of magnet?

Yes, the Lenz force can accelerate any type of magnet as long as it is placed in a changing magnetic field. This includes permanent magnets, electromagnets, and even magnetic materials such as iron or steel.

## 4. How is the direction of the Lenz force determined?

The direction of the Lenz force is determined by the direction of the changing magnetic field. The induced current will always create a magnetic field that opposes the changing magnetic field, so the direction of the Lenz force will be in the opposite direction of the changing magnetic field.

## 5. What are some real-world applications of the Lenz force?

The Lenz force has many practical applications, including electric generators, electric motors, and magnetic brakes. It is also used in induction heating, which is the process of heating a conductive material by inducing an electric current in it using a changing magnetic field.