# Charge density seen from a moving reference frame S' (SR + EM)

• LCSphysicist
In summary, the conversation discusses finding the charge density in the S' frame. One method suggested is to calculate the electric field and use the formula for charge density, while another method involves expressing the charge density in terms of the number of positive charges and free electrons per unit length. The idea of length contraction is also mentioned as a way to transform these quantities between the S and S' frames.
LCSphysicist
Homework Statement
a cable infinite and very thin that carries current and has charge density
null in the reference of fixed positive charges, in addition, consider a
charge particle q positioned at a distance l from the cable and traveling
in parallel direction to the cable with the same speed (relativistic) u
of the electrons in the cable.
Relevant Equations
.
There are some question involving the statement. One of them is about the charge density in S' frame. It asks to calc it.

I thought that i could calculate the electric field in the referencial frame S' and, then, use the formula
$$E = \lambda / 2 \pi \epsilon l$$
In that way, i would obtain ##\lambda##. Is that a reasonable way to find the charge density? Is there another way?

Last edited by a moderator:
Herculi said:
I thought that i could calculate the electric field in the referencial frame S' and, then, use the formula $$E = \lambda /( 2 \pi \epsilon l)$$
In that way, i would obtain ##\lambda##. Is that a reasonable way to find the charge density?
Yes.

Herculi said:
Is there another way?
You can express ##\lambda## in terms of ##n_p## and ##n_e##, where ##n_p## is the number of positive charges per unit length of the cable and ##n_e## is the number of free electrons per unit length. Use the idea of length contraction to see how ##n_p## and ##n_e## transform when switching from frame S to frame S'.

[Edited in order to improve notation.]

Last edited:

## 1. What is charge density seen from a moving reference frame?

In the context of Special Relativity (SR) and Electromagnetism (EM), charge density seen from a moving reference frame refers to the measure of electric charge per unit volume as observed by an observer in a frame of reference that is moving relative to the charge. This is a concept that arises from the Lorentz transformation equations, which describe how physical quantities, such as charge density, appear to change when viewed from different reference frames.

## 2. How does charge density change in a moving reference frame?

According to the Lorentz transformation equations, when an observer in a stationary reference frame measures the charge density of a moving object, they will observe a different value compared to an observer in a reference frame that is moving with the object. This is due to the phenomenon of length contraction, which causes the distance between charged particles to appear shorter in the moving frame, resulting in a higher charge density.

## 3. What is the relationship between charge density and electric field in a moving reference frame?

In a stationary reference frame, the electric field is directly proportional to the charge density. However, in a moving reference frame, the electric field is not only affected by the charge density but also by the relative motion between the observer and the charged particles. This is described by the magnetic field component of the electromagnetic force, which is dependent on the velocity of the observer.

## 4. How does the concept of charge density seen from a moving reference frame relate to the theory of Special Relativity?

The concept of charge density seen from a moving reference frame is a consequence of the theory of Special Relativity, which states that the laws of physics are the same for all observers in uniform motion. This means that the observed values of physical quantities, such as charge density, will depend on the reference frame of the observer and can be transformed using the Lorentz transformation equations.

## 5. Can charge density be observed directly from a moving reference frame?

No, charge density cannot be observed directly from a moving reference frame. This is because the observer in the moving frame is also subject to the same physical laws and transformations as the charged particles, making it impossible to measure the charge density without taking into account the observer's velocity and frame of reference. Instead, the concept of charge density seen from a moving reference frame is a theoretical construct used to explain the effects of relative motion on electric charge.

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