# Reaction Force of Lorentz Force

• Wein_Sim
In summary, the Lorentz Force is a force that acts on charged particles in an electric field. The Third Law does not always hold in electrodynamics, which is the scientific study of the interaction of electric and magnetic fields.
Wein_Sim
Hi everyone,
in school we recently learned about the Lorentz Force, which says that when charged particles move through an electric field (perpendicular to the field lines), a force is excerted on them (called the Lorentz Force), which goes perpendicular to both the magnetic field lines and the direction in which the charged particels are moving.
But Newton's third Law says that every force has an equal and opposite reaction force. And so I asked my teacher what that reaction force for the Lorentz Force is but he didn't know the answer. Does anyone of you know?
Simon

PeroK
Wein_Sim said:
what that reaction force for the Lorentz Force is
The force acts on whatever produces the Field. It's the same idea as the force that acts on the Earth, pulling it towards us with our 'weight' force.
The Coulomb Force is between two charges whilst the Lorenz Force is on one of those charges in the Field produced by the other charge. Just two ways of looking at the same Force.

sophiecentaur said:
The force
Do you mean the Lorentz Force or the Reaction Force?
sophiecentaur said:
whatever produces the Field
Do you mean the electric field or the magnetic field?
sophiecentaur said:
the force that acts on the Earth
Ok yeah for gravity it makes sence, since there are two object involved, but for the Lorentz Force it seems a little weird, because in school we only talked about the force on the particles and nothing else

Wein_Sim said:
Hi everyone,
in school we recently learned about the Lorentz Force, which says that when charged particles move through an electric field (perpendicular to the field lines), a force is excerted on them (called the Lorentz Force), which goes perpendicular to both the magnetic field lines and the direction in which the charged particels are moving.
But Newton's third Law says that every force has an equal and opposite reaction force. And so I asked my teacher what that reaction force for the Lorentz Force is but he didn't know the answer. Does anyone of you know?
Simon

Analysing Newton's third law and the electromagnetic force is not so simple. You could look on line for a discussion of this. E.g.

https://physics.stackexchange.com/questions/138095/Newtons-third-law-exceptions
In summary, in electrostatics and magnetostatics the Third Law holds (although it's not always easy to verify this); but, in electrodynamics the Third Law does not hold. Momentum is conserved in electrodynamics, but only when you consider momentum stored in the EM fields themselves and not only the momentum of the particles.

@PeroK Ok, thank you for the answer

To see how Newton's law plays out, it might help to see an experiment that separates the individual forces that combine to produce the Lorentz force: (qV X B) + qE

Here are two short YouTube videos that only take a few seconds to watch.

The first link below shows the MAGNETIC part of the Lorentz force. A wire is dangled down horizontally (like a trapeze) in front of a magnet. The wire jumps toward the magnet when you turn on the current. That's the (qV X B) part of the force. Newton's Laws are also working-- the charges exert an equal & opposite force on the magnet, but the giant magnet is fixed in place, so you can't see it move. If you were shrunk down to the size of an action figure, sat on the trapeze, and tied a string between your hand and the magnet, you could also make the wire swing move, but the magnet would not seem to move; But Newton is still working.

The second link shows moving ELECTRIC field part of the Lorentz force. Electric charges (moving in a beam) are pushed around in an electric field. Watch the video for 1 full minute to see the the electric field (E) pushing charges both ways. Electric field (E) is VERTICAL, so the charges are pushed vertically, in the direction of E. The electron beam wants to go straight, but you can see the electrons being pushed around pretty hard, so they are pushing back (equal/opposite force) on the the Lego-sized metal blocks (plates) that create the E field. But those are fixed in place, so you can't really see it move. It's like a friend pushing you around if you were trying to hold your ground. If they are pushing on you, then you are pushing back with an equal/opposite force, regardless of who is moving & who is not.

Hope that helps!

## 1. What is the Reaction Force of Lorentz Force?

The Reaction Force of Lorentz Force is the equal and opposite force that is exerted on a charged particle when it experiences a magnetic force. This force is a result of Newton's Third Law of Motion.

## 2. How is the Reaction Force of Lorentz Force calculated?

The Reaction Force of Lorentz Force can be calculated by using the formula F = qvB, where F is the force, q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field strength.

## 3. What is the direction of the Reaction Force of Lorentz Force?

The direction of the Reaction Force of Lorentz Force is always perpendicular to both the magnetic field and the velocity of the charged particle. This means that the force will be either towards or away from the source of the magnetic field, depending on the direction of the particle's velocity.

## 4. How does the Reaction Force of Lorentz Force affect the motion of a charged particle?

The Reaction Force of Lorentz Force can change the direction of a charged particle's motion, causing it to move in a circular path or to deviate from its original path. It can also cause the particle to speed up or slow down, depending on the direction of the force.

## 5. What are some real-life applications of the Reaction Force of Lorentz Force?

The Reaction Force of Lorentz Force is used in various technologies, such as electric motors, particle accelerators, and MRI machines. It is also important in understanding the behavior of charged particles in space, such as in the Earth's magnetic field and the solar wind.

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