Parallel line currents & Lorentz transformation

In summary, the conversation discusses two parallel infinite line currents with equal magnitudes and how they attract each other. Moving to a different frame of reference, K', where the current is zero, results in a purely electrical force instead of a purely magnetic one. However, even in this frame, the currents should still repel each other due to the symmetry between the two lines.
  • #1
Preno
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0
Okay, I'm sure I must have overlooked something very trivial, so please help me with this:

Two parallel infinite line currents of equal magnitude attract each other. The current can be thought of as consisting of positive and negative particles with equal linear densities, but each moving with a different velocity (wlog let's assume the positive ones are static in some frame of reference K). Let us now move to the frame of reference K' which moves with the current so that the current in K' is zero. The force which was purely magnetic in K is now replaced with a purely electrical one - the linear densities of the positive and negative particles undergo Lorentz transformation, so that the total density in K' is non-zero.

Here's my problem: if linear densities and the velocities of particles (and hence the currents) have the same magnitude in K, then they must also have the same magnitude in K' (the transformation respects the symmetry between the two lines). But like charges repel each other. So it would seem that in K' (hence also in K), the currents actually repel each other.
 
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  • #2
Hi Preno! :smile:
Preno said:
The current can be thought of as consisting of positive and negative particles with equal linear densities, but each moving with a different velocity …
Let us now move to the frame of reference K' which moves with the current so that the current in K' is zero. …

Sorry, I'm not following what K' is …

as you say, there are two lots of charge, moving with a different velocity. :confused:

(and don't forget the Lorentz-Fitzgerald length-contraction)
 
  • #3
tiny-tim said:
Hi Preno! :smile:


Sorry, I'm not following what K' is …
K' is the frame in which the current vanishes.
as you say, there are two lots of charge, moving with a different velocity. :confused:
Well, the line is electrically neutral, so there need to be both positive and negative charges.
(and don't forget the Lorentz-Fitzgerald length-contraction)
No, I'm not forgetting it. That's the whole point. The linear density of those charges changes when transforming to K' but it remains the same on both lines. Hence they should repel each other.
 

1. What are parallel line currents?

Parallel line currents refer to two or more electrical currents that are flowing in parallel and in the same direction. This means that the currents are aligned and are not intersecting or crossing each other.

2. How do parallel line currents behave in relation to each other?

Parallel line currents are subject to the laws of electromagnetism, specifically the Lorentz force law. This states that parallel currents will experience a force that is perpendicular to both currents. The direction of this force is determined by the direction of the currents and can either attract or repel the currents from each other.

3. What is the significance of Lorentz transformation in relation to parallel line currents?

Lorentz transformation is a mathematical concept that describes the relationship between two different frames of reference in space and time. In the context of parallel line currents, it is used to calculate and predict the behavior of the currents in different reference frames, such as moving or rotating frames.

4. How does the distance between parallel line currents affect their behavior?

The distance between parallel line currents can affect their behavior in several ways. As the distance increases, the force between the currents decreases according to the inverse-square law. Additionally, a larger distance can also lead to a decrease in the magnetic field created by the currents.

5. Can parallel line currents ever intersect or cross each other?

No, by definition, parallel line currents are always aligned and do not intersect or cross each other. If two currents do cross, they are not considered parallel line currents and will behave differently according to the principles of electromagnetism.

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