# Electromagnetic Force in Special Relativity

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• L0r3n20
In summary: The force experienced by a ferromagnetic object in one frame is not the same in the other frame, as the force depends on the internal charges and currents, which need to be properly transformed. In summary, the Lorentz transformation leads to a shift in the electric field and the appearance of a new magnetic field in the moving frame, and the magnetization and polarization are also affected. The force experienced by the object is not the same in the two frames and depends on the transformed internal charges and currents.
L0r3n20
Hi! I came out with a problem last night I wasn't able to solve:

Let's assume we have a condensator with a uniform electric field E confined in its inside, lying on the z axes. Let's also assume we have a piece of a ferromagnetic object aligned with the condensator at time t = 0, on the y-axes. We now perform a boost along the x-axes for both the object: we will find the electric field shifted by a gamma factor and a new magnetic field along the y-axes. So, in the moving frame, the ferromagnetic object would now feel a force toward the condensator.
I cannot understand how this is possible being the Lorentz transformation a switch among inetrial frames.

Don't forget to transform the ferromagnetic object too!

Do I have to transform every magnetic domain? Aren't they negligible?

L0r3n20 said:
Do I have to transform every magnetic domain? Aren't they negligible?
The force on an object depends on the internal charges and currents. Not only on the EM field. Charge and current densities also need to be properly transformed.

L0r3n20 said:
Do I have to transform every magnetic domain? Aren't they negligible?
Clearly they are not negligible in this problem.

The electric field and the magnetic field are components of the electromagnetic field tensor, so what is purely an electric field in one frame becomes both an electric and a magnetic field in another frame. Similarly the magnetization and polarization are components of the magnetization-polarization tensor, so what is purely magnetization in one frame becomes both magnetization and polarization in another frame.

## 1. What is electromagnetic force in special relativity?

Electromagnetic force in special relativity refers to the fundamental force that exists between electrically charged particles. It is described by the theory of special relativity, which explains how electromagnetic fields and forces are affected by the relative motion of objects.

## 2. How does special relativity affect electromagnetic force?

In special relativity, the concept of simultaneity is relative and the laws of physics are the same for all observers in uniform motion. This means that the strength and direction of the electromagnetic force may appear different to different observers depending on their relative motion, but the underlying principles remain the same.

## 3. What is the relationship between electricity and magnetism in special relativity?

Special relativity shows that electric and magnetic fields are two aspects of the same phenomenon. Moving electric charges create magnetic fields, and changing magnetic fields create electric fields. This relationship is described by Maxwell's equations and is fundamental to understanding electromagnetic force in special relativity.

## 4. How does the speed of light impact electromagnetic force in special relativity?

According to special relativity, the speed of light is the same for all observers regardless of their relative motion. This means that the strength of the electromagnetic force between two charged particles will appear the same to all observers as long as they are moving at a constant speed relative to each other.

## 5. What are some real-world applications of electromagnetic force in special relativity?

Electromagnetic force plays a crucial role in many modern technologies, such as electric motors, generators, and power plants. It also underlies the functioning of electronic devices like computers and cell phones. Additionally, special relativity and the principles of electromagnetic force are essential for understanding and developing technologies such as particle accelerators and nuclear reactors.

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