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

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?

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Homework Helper
Gold Member
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.

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.]

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