Exploring Newton's Third Law in an Imaginary Magnetic Field

In summary, when the coil is switched off, the charged particle experiences a force that reacts directly on the magnet.
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pays_fan
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Hi, here's a theoretical problem that I am trying to find a satisfactory answer for.

Imagine a coil that is temporarily switched on an off and generates a magnetic field that permeates through space. Now imagine a charged particle passing through this field, at time that the coil is already switched off, and experiencing electromagnetic force. I would assume that the coil would not experience a reactive force because it is switched off (or for the sake of argumentation, it can even be disassembled by the time the charged particle experiences the magnetic field). How is this in line with Netwon's third law?
 
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pays_fan said:
a magnetic field that permeates through space
The word ”propagates” would probably be a better fit for what you want to say here. To permeate can also be taken to mean to exist everywhere.

If I understand your question correctly, you want to consider the a field pulse that propagates outwards and is of finite extent in time.

In an interaction with the electromagnetic field, Newton’s third law holds locally for the interaction between the paricle and the field itself. The electromagnetic field carries energy and momentum. This is described by the electromagnetic stress energy tensor. Newton’s third law also holds for the interaction between the coil and the field when the pulse was generated.
 
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Orodruin said:
In an interaction with the electromagnetic field, Newton’s third law holds locally for the interaction between the particle and the field itself. The electromagnetic field carries energy and momentum. This is described by the electromagnetic stress energy tensor. Newton’s third law also holds for the interaction between the coil and the field when the pulse was generated.
Yes, Feynman showed an example in his Lectures on Physics Volume II page 26-5 fig 26-6 that two charged particles can move in such a way that their forces are not always equal and opposite.
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Fig. 26–6. The forces between two moving charges are not always equal and opposite. It appears that “action” is not equal to “reaction.”

https://www.feynmanlectures.caltech.edu/II_26.html
 
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If the charge is in the radiated field from the magnet then it will experience an accelerating force. It seems to me that it will radiate a new wave opposing the incoming wave, in the manner of a conductor.
 
  • #5
Radiation by the magnet implies that the magnet has a finite length. If the charge is very close to such a magnet, it will primarily experience the induction field of the magnet and so it is different to the case for the radiation field. When the current is turned off, the charge will now be in the E field caused by the collapsing magnetic field, and will experience a force. As far as I can see, this force will react directly on the magnet with zero propagation delay.
 

Related to Exploring Newton's Third Law in an Imaginary Magnetic Field

1. What is Newton's Third Law?

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

2. How does this law apply to an imaginary magnetic field?

In an imaginary magnetic field, the same principle applies. When a magnet exerts a force on another magnet, the second magnet will exert an equal and opposite force back on the first magnet. This is because magnets have opposite poles (north and south) that attract and like poles that repel, creating a balanced force.

3. Can you give an example of Newton's Third Law in an imaginary magnetic field?

Imagine two magnets placed near each other in an imaginary magnetic field. When the north pole of one magnet is brought close to the south pole of the other magnet, they will attract each other. This is because the north pole exerts a force on the south pole, and the south pole exerts an equal and opposite force back on the north pole.

4. How does the strength of the force in an imaginary magnetic field relate to Newton's Third Law?

According to Newton's Third Law, the strength of the force in an imaginary magnetic field will always be equal and opposite. This means that if one magnet exerts a strong force on another magnet, the second magnet will also exert a strong force back on the first magnet.

5. Are there any real-life applications of exploring Newton's Third Law in an imaginary magnetic field?

Yes, there are many real-life applications of this concept. For example, it helps us understand the behavior of magnets and how they interact with each other. This knowledge is essential in the development of technologies such as MRI machines, electric motors, and generators.

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