# Magnetic Fields and Lorentz force flaw

• xfshi2000
In summary: Why doesn't it generate electric field? that is to say, particle with charge q only feel magnetic force and no coulomb force?The explanation given in the original post applies here as well- charges under different reference frames have different densities of positive and negative charge, so there is a net force of attraction (coulomb force) between them in the rest frame, but not in the moving frame.
xfshi2000
HI all:
I have one confused question. a infinitely long wire carrying constant direct current is placed in the space. One particle with charge q and velocity v is moving in the magnetic field which is created by current-carrying wire. We know in the lab frame. particle will accelerate in this magnetic field and feel a lorentz force(F=(q/c)(vxB)). Now if we switch from lab reference frame to the rest frame of particle, in this rest frame, particle speed is zero. that means Lorentz force disappear. According F=q[E+1/c(vxB)]. A electrostatic field must appear.
1) What is origin of this electric field? How does it generate?
One mentions that positive charge and negative charge density in the wire are different value under different reference frame.
For a line charge with length L, the electric field E=Q(1/r^2-L^2/2r^4). Because total charge are conserved. The first term is unaffected by choosing different reference frame. For the second term, they show length contraction in different reference frame. That is why they have different positive and negative charge density in the wire under different reference frame.
In our lab frame, due to constant direct current in the wire, I assume positive charge density is larger than negative charge density.
2) Why doesn't it generate electric field? that is to say, particle with charge q only feel magnetic force and no coulomb force?
Does anyone give me detail explanation? thanks a lot

xfshi2000 said:
HI all:

Now if we switch from lab reference frame to the rest frame of particle, in this rest frame, particle speed is zero. that means Lorentz force disappear. According F=q[E+1/c(vxB)]. A electrostatic field must appear.

Just a simple question: Suppose you made a mark on the wire. Wouldn't the particle see the mark receding from it, and therefore the magnetic field in motion with respect to it so the Lorentz force would, in fact, not be zero?

You might find the first paragraph of Einstein's paper on Special Relativity interesting reading...

xfshi2000 said:
in this rest frame, particle speed is zero. that means Lorentz force disappear. According F=q[E+1/c(vxB)]. A electrostatic field must appear.
1) What is origin of this electric field? How does it generate?
In short, it comes from length contraction. See http://physics.weber.edu/schroeder/mrr/MRRtalk.html for details.

Feynman does a great job with this particular example. See Vol II, 13.6 of the Lectures.
A similar problem: 2 (+) charges at rest repel each other, but viewed from a moving frame, they also feel a Lorentz B attraction...
Follow-up: What's different for gravity??

## 1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges, such as those found in electrons, protons, and other particles.

## 2. How is a magnetic field represented?

A magnetic field is represented by lines of force, also known as magnetic field lines. These lines indicate the direction and strength of the magnetic field at any given point.

## 3. What is the Lorentz force flaw?

The Lorentz force flaw, also known as the Lorentz force paradox, is a theoretical inconsistency in classical electromagnetism. It arises when considering the force on a charged particle moving in a magnetic field, as described by the Lorentz force equation.

## 4. How does the Lorentz force flaw affect our understanding of magnetic fields?

The Lorentz force flaw challenges our understanding of the fundamental principles of electromagnetism, as it suggests that the force on a charged particle in a magnetic field is dependent on the frame of reference. This goes against the basic principle of relativity and raises questions about the nature of magnetic fields.

## 5. Is the Lorentz force flaw still relevant in modern physics?

Yes, the Lorentz force flaw is still a topic of debate and research in modern physics. While it has been largely resolved through the development of quantum mechanics and special relativity, there are still aspects of the paradox that remain unresolved and continue to be studied by scientists.

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