Conceptual Aspect of Relativity: Electric & Magnetic Forces

[Ja4Coltrane]

I am giving a little lecture on the conceptual aspect of relativity tomorrow and was wondering something.
Consider a wire carying positive charges moving to the right and negative charges moving to the left. Say that a positive charge is placed above the wire and this positive charge moves at the some velocity as the positive charges within the wire.
Now I know that what happens is from the frame of the negative charges there is a magnetic force and from the frame of the positive charges there is an electric force due to length contraction acting on the free positive charge but my question is this: why doesn't length also contract for the frame of the negative charges? It seems to me that the positive charges should contract and therefore create an electric force which opposes the magnetic force. Does it have something to due with the fact that the charge on top is moving too? Any help is GREATLY appreciated.

 

[pervect]

You should, in general, expect there to be exacty one frame in which the electric field is zero.

In your example, you are assuming that this is a frame where the positive charges are moving right and the negative charges are left.

Therefore you are correct in thinking that there will be electric fields in both a frame comoving with the positive charges and a frame comoving with the negative charges.

What you probably want to do is therefore work out the total force (electric and magnetic) and show that it transforms covariantly.

To do that, one of the things you need to know how forces should transform under special relativity. I'm assuming that you do know this or that at least it would do you some good to think about it. If you don't know or get stuck, ask some more questions.

 

[Entropia]

The conceptual aspect of relativity in the context of electric and magnetic forces is a very interesting and complex topic. Your question about the length contraction for the frame of the negative charges is a valid one and shows that you are thinking critically about the subject.

To answer your question, we need to consider the fundamental principles of relativity and how they apply in this scenario. The first principle is that the laws of physics are the same for all observers in uniform motion. This means that the behavior of the positive charges in the wire and the positive charge placed above the wire should be the same, regardless of their relative velocities.

The second principle is that the speed of light is constant in all inertial frames of reference. This means that the speed of light is the same for all observers, regardless of their relative motion. This principle is what leads to the phenomenon of length contraction and time dilation in relativity.

Now, let's apply these principles to the scenario you have described. From the frame of the negative charges, the positive charges in the wire are moving to the right and the positive charge placed above the wire is also moving to the right at the same velocity. This means that, from the perspective of the negative charges, the positive charge above the wire is not length contracted. This is because the speed of light is constant for all observers, and the positive charge above the wire is moving at the same velocity as the negative charges.

On the other hand, from the frame of the positive charges, the positive charge above the wire is moving to the left. This means that, from the perspective of the positive charges, the positive charge above the wire is length contracted. This is because the speed of light is constant for all observers, and the positive charge above the wire is moving at a different velocity than the positive charges in the wire.

So, to answer your question, the length contraction for the frame of the negative charges does not occur because the positive charge above the wire is also moving and therefore, the speed of light is the same for both frames of reference. This leads to the electric and magnetic forces being equal and opposite, resulting in a balanced system.

I hope this helps to clarify the conceptual aspect of relativity in relation to electric and magnetic forces. Keep thinking critically and asking questions, as this is the key to understanding complex concepts in physics. Good luck with your lecture!