# If a magnet does not feel the Lenz force, will there be a violation of energy?

• hemalpansuriya
In summary: From magnet's perspective, charge is moving towards it. Magnet will see that velocity of charge and Magnetic field is zero, so there is no lorenz force on charge ( q(v×b)). So there will no opposite force on magnet. Magnet will see that the force on charge is only due to changing magnetic field.
hemalpansuriya
Consider the following, a magnet and a charge is attached to a platform, which is constrained to move only up and down direction. Now, if magnet is moved towards charge, due to changing magnetic field, an electric field will be created. This electric field will impart force on charge. since the magnet and charge are attached on a same platform and platform can move only up and down, magnet will not experience lenz force. But the whole platform will move up ( or down according to electric field direction ). So, we are getting work from system but magnet will not experience lenz force as it will also move with the charge. Will it violate energy conservation ?

No system which follows Maxwells equations can violate the conservation of energy.

Would you explain me how it will conserve for this particular case ?

hemalpansuriya said:
This electric field will impart force on charge.
Then there will be an equal and opposite force on the magnet.

Dale said:
No system which follows Maxwells equations can violate the conservation of energy.
And the Lorentz force law.

Dale
hutchphd said:
Then there will be an equal and opposite force on the magnet.
How can an opposite force act on Magnet in this case ? ...when you have a magnet and coil, there is only lenz force which acts on the magnet which will resist the motion of magnet. But in this case there is no lenz force and no other opposite force also.

hemalpansuriya said:
How can an opposite force act on Magnet in this case ? ...when you have a magnet and coil, there is only lenz force which acts on the magnet which will resist the motion of magnet. But in this case there is no lenz force and no other opposite force also.
The magnet will "see" a moving charge which produces a magnetic field.

hemalpansuriya said:
Would you explain me how it will conserve for this particular case ?
I can do better than that. I can explain how it is conserved for all possible cases. See here:

http://farside.ph.utexas.edu/teaching/jk1/lectures/node10.html
The application to your specific scenario is left as an exercise for the interested reader.

vanhees71 and Michael Price
hutchphd said:
The magnet will "see" a moving charge which produces a magnetic field.
magnet will see charge coming towards it, but it will not exert force since the angle between velocity and magnetic field is zero ( lorenz force f = q(v×b) ).

A permanent magnet is a complicated object containing internal " currents". (Two magnets are attracted when neither of them is moving, for instance).
I was pointing out that equally disturbing in your initial premise was the violation of Newtons Laws. Your premise is false.

The whole reason that we do general proofs, like the one I posted above, is that analyzing particular scenarios can be tricky. We can do a general analysis and know that energy is always conserved no matter what, for any scenario that obeys Maxwell’s equations. The complicated details of any particular scenario are irrelevant.

I am not even clear on the actual scenario proposed, but it doesn’t matter. Energy is provably conserved regardless.

The OP's contention seems to be that the electric dipole character of the "magnetic" field of a moving magnet will cause a force on the charge.

But where does this dipole field come from? "The fields transform like that" isn't an answer (or only half an answer, anyway). There needs to be a source term for an electric field, or else Maxwell's equations don't hold in this frame. The answer is that the magnet itself, viewed in a frame where it is moving, is a little bit of an electric dipole. So it will feel a force from the Coulomb field of the charge. Thus the platform won't move.

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Ibix said:
The OP's contention seems to be that the electric dipole character of the "magnetic" field of a moving magnet will cause a force on the charge.

But where does this dipole field come from? "The fields transform like that" isn't an answer (or only half an answer, anyway). There needs to be a source term for an electric field, or else Maxwell's equations don't hold in this frame. The answer is that the magnet itself, viewed in a frame where it is moving, is a little bit of an electric dipole. So it will feel a force from the Coulomb field of the charge. Thus the platform won't move.
From magnet's perspective, charge is moving towards it. Magnet will see that velocity of charge and Magnetic field is zero, so there is no lorenz force on charge ( q(v×b)). So there will no opposite force on magnet. Magnet will see that the force on charge is only due to changing magnetic field. Energy will only conserve if lenz force will act on magnet, which is not applicable in this case.

hemalpansuriya said:
From magnet's perspective, charge is moving towards it.
In the magnet's rest frame the charge is moving, yes, so generates a magnetic field that creates a force on the magnet. Thus the platform does not move.

Ibix said:
In the magnet's rest frame the charge is moving, yes, so generates a magnetic field that creates a force on the magnet. Thus the platform does not move.
Yes, Charge generates magnetic field. But calculate the lorentz force, it will be zero. As ( v×B) is zero. So, magnet can not get opposite force.

hemalpansuriya said:
Yes, Charge generates magnetic field. But calculate the lorentz force, it will be zero. As ( v×B) is zero. So, magnet can not get opposite force.
Just to be clear: here you are saying that a magnet does not apply a force to another magnet that is not co-linear with it. Is my understanding of your position correct? If so, could you explain how a compass works?

Ibix said:
Just to be clear: here you are saying that a magnet does not apply a force to another magnet that is not co-linear with it. Is my understanding of your position correct? If so, could you explain how a compass works?
Just consider force on a magnet by a current carrying conductor which is perpendicular to magnet's north or south pole. Since ( V×B) is zero, no force on conductor and hence, no force on magnet.

hemalpansuriya said:
Just consider force on a magnet by a current carrying conductor which is perpendicular to magnet's north or south pole. Since ( V×B) is zero, no force on conductor and hence, no force on magnet.
The charge is not above either pole of the magnet as I understand your setup.

Ibix said:
The charge is not above either pole of the magnet as I understand your setup.
In my setup, magnet's north or south pole ( whatever you can choose ) is moving towards charge.

hemalpansuriya said:
In my setup, magnet's north or south pole ( whatever you can choose ) is moving towards charge.
In that case the magnetic field at the charge is parallel to the motion, and there is no electric field contribution from the magnet nor magnetic contribution from the charge. From symmetry there is clearly no transverse force on either the magnet or the charge and the platform does not move.

hemalpansuriya said:
a magnet and a charge is attached to a platform, which is constrained to move only up and down direction. Now, if magnet is moved towards charge
Hold on. If the magnet and the charge are both attached to the platform, then how can the magnet move towards the charge?

hemalpansuriya said:
From magnet's perspective, charge is moving towards it.
How? Aren’t they both attached to the platform?

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Dale said:
The impression I have now is that the platform is better described as a tube, with a charge attached at one end and a bar magnet inside it at the other end and free to slide along the length of the tube. The tube is constrained somehow (attached to a cart on rails, perhaps) so that it may move freely perpendicular to its length.

The OP's contention is that pushing the bar magnet along the tube causes a force on the charge that makes the tube move along the rails. Since the fields are axisymmetric in this case (at least for all frames with velocities parallel to the tube) this is clearly wrong just from symmetry. And, in fact, boosts in that direction do not change the E and B field strengths on axis, where both the charge and magnet lie (excepting a possible transient when the magnet is accelerated), so I don't understand where he thinks the Lorentz force he's worried about comes from (it's zero in this case). Nevertheless, he did confirm that everything is colinear.

hemalpansuriya said:
In my setup, magnet's north or south pole ( whatever you can choose ) is moving towards charge.
If the magnet is moving, there's also an electric field!

vanhees71 said:
If the magnet is moving, there's also an electric field!
Not on axis if its movement is parallel to the axis of the magnet. But even if there were, it wouldn't cause a transverse force.

Ibix said:
Not on axis if its movement is parallel to the axis of the magnet. But even if there were, it wouldn't cause a transverse force.
As magnet moves, charge experiences change in magnetic field. So, there is an electric field produced in peripheral direction of tube. If charge is happened to be slightly a side to the center of tube, then it will experience a force. Since charge is attached and tube also constrained to move perpendicular direction of length, it will move. But magnet will not feel any lenz force, which we have in our normal interaction of magnet and coil.

Dale said:
Hold on. If the magnet and the charge are both attached to the platform, then how can the magnet move towards the charge?

How? Aren’t they both attached to the platform?

Magnet can move towards charge. But it is constrained not to leave surface of platform. You can think of a track on which magnet moves towards charge.

hemalpansuriya said:
Magnet can move towards charge. But it is constrained not to leave surface of platform. You can think of a track on which magnet moves towards charge.
So the platform moves up and down and the magnet slides left and right on the platform? With the pole of the magnet oriented towards the charge.

Yes, this is precisely the sort of scenario that the general proof is valuable for.

Dale said:
So the platform moves up and down and the magnet slides left and right on the platform? With the pole of the magnet oriented towards the charge.

Yes, this is precisely the sort of scenario that the general proof is valuable for.
I know general proof. But I am wondering if there is no reaction force ( Lenz force ) on the magnet, what will conserve energy in this case.

hemalpansuriya said:
I know general proof. But I am wondering if there is no reaction force ( Lenz force ) on the magnet, what will conserve energy in this case.
I am not at all convinced that there is no reaction force. Clearly since your specific analysis contradicts the general proof your specific analysis is wrong. I suspect that it is the suggestion that there is no force on the magnet which is incorrect.

hemalpansuriya said:
As magnet moves, charge experiences change in magnetic field. So, there is an electric field produced in peripheral direction of tube. If charge is happened to be slightly a side to the center of tube, then it will experience a force.
OK. Note that this is not the original scenario you specified, nor the second one, since the magnet is not moving towards the charge - rather, it's moving past the charge.

I'd suggest investigating the Poynting vector associated with the joint EM field of the charge and magnet. I rather suspect you'll find that it's not symmetric about the plane containing the magnet's velocity vector and the charge. Thus the EM field carries momentum away in one direction, which will conserve momentum.

I also note that the energy density of the field is unlikely to be constant with time. What's the total energy in the field? Does it change? If so, you have a likely source for any work.

Finally, if there is a net lateral force on the charge, then in the charge rest frame the magnet will not be moving along its symmetry axis and I would expect it to acquire an electric dipole character, which will feel a force from the field of the charge.

## 1. What is the Lenz force?

The Lenz force is an electromagnetic force that acts on a conductor when it is placed in a changing magnetic field. It is responsible for producing eddy currents in the conductor, which in turn creates a counter magnetic field that opposes the original magnetic field.

## 2. How does the Lenz force relate to energy conservation?

The Lenz force is directly related to the principle of energy conservation. In accordance with Faraday's law of induction, the Lenz force opposes any change in the magnetic field, which means it also opposes any change in the energy of the system. This ensures that energy is conserved in the system.

## 3. Can a magnet really not feel the Lenz force?

In theory, a magnet that is not moving or changing in any way will not experience the Lenz force. However, in practical situations, there is always some degree of movement or change in the magnetic field, so the Lenz force will always be present to some extent.

## 4. What happens if a magnet does not feel the Lenz force?

If a magnet does not feel the Lenz force, it means that there is no change in the magnetic field or the energy of the system. This could happen if the magnet is completely stationary and there are no external forces acting on it. In this case, the Lenz force would not be necessary to conserve energy.

## 5. Is it possible for the Lenz force to be violated?

No, the Lenz force cannot be violated. It is a fundamental law of electromagnetism and has been proven through numerous experiments. Any violation of the Lenz force would also violate the principle of energy conservation, which is a fundamental law of physics.

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