Why does magnetic field depend on angle?

[Electric to be]

In addition, why is there no magnetic field along the line of motion of a charge? If length contraction occurs along this line of motion, I don't see why there is no magnetic field created along this line of motion for other charges to interact to. I get magnetism is fundamental, but at least getting some intuition from relativity, length contraction should also occur along this line (and as a result in some frame people should see the length contraction and increased electric force as a magnetic force in other frames?)

 

[Hornbein]

In addition, why is there no magnetic field along the line of motion of a charge? If length contraction occurs along this line of motion, I don't see why there is no magnetic field created along this line of motion for other charges to interact to. I get magnetism is fundamental, but at least getting some intuition from relativity, length contraction should also occur along this line (and as a result in some frame people should see the length contraction and increased electric force as a magnetic force in other frames?)

Magnetic field is essentially a sideways motion due to corrections for relativity. If its coming straight toward or away, then no sideways motion.

 

[Orodruin]

As already stated in your other thread on the subject, you cannot and should not think of electromagnetic fields using length contraction as an argument.

 

[Electric to be]

As already stated in your other thread on the subject, you cannot and should not think of electromagnetic fields using length contraction as an argument.

Maybe, and I'm sorry if I come off as stubborn or ignorant but I've seen a lot of convincing arguments that I can, at least roughly. Maybe if you could explain why not?For example:

What if I have a negative charge, a positive charge and another positive in a line. Say the two positive charges have the same velocity. All the charges are equally spaced so the middle positive charge has no electric force, and no magnetic since they are on the same line. However, in the positive charges frame, the distance between the two positive charges has increased and the distance between the middle and the negative charge has decreased. Thus, still no magnetic force, but a net electric force. Is this not a contradiction?

 

[Electric to be]

Magnetic field is essentially a sideways motion due to corrections for relativity. If its coming straight toward or away, then no sideways motion.

Well why exactly does it have to be sideways? Refer to my example above.

 

[Orodruin]

Maybe, and I'm sorry if I come off as stubborn or ignorant but I've seen a lot of convincing arguments that I can, at least roughly. Maybe if you could explain why not?

Because the EM field is a rank 2 anti-symmetric tensor and transforms accordingly. There are some result which give you effects which you might interpret as similar to length contraction, but you cannot go from there to using it as your main argument or use it to try to make deductions.

All the charges are equally spaced so the middle positive charge has no electric force, and no magnetic since they are on the same line.

Wrong. Since the positive charges are moving their electric fields are different than the simple 1/r^2.

 

[Electric to be]

Because the EM field is a rank 2 anti-symmetric tensor and transforms accordingly. There are some result which give you effects which you might interpret as similar to length contraction, but you cannot go from there to using it as your main argument or use it to try to make deductions.
Wrong. Since the positive charges are moving their electric fields are different than the simple 1/r^2.

So does the magnetic field also vary than the simple 1/r^2. But it already varies with speed. Egh this is confusing..

So do I just accept that the magnetic field is a fact of nature and randomly particles that aren't in line with a moving particle have a force acted on them?

 

[Orodruin]

So does the magnetic field also vary than the simple 1/r^2. But it already varies with speed. Egh this is confusing..

So do I just accept that the magnetic field is a fact of nature and randomly particles that aren't in line with a moving particle have a force acted on them?

There is nothing random here. It is well described by a beautiful relativistically invariant theory. You might have to learn more about how it works and how it is described before you can appreciate it though.

 

[Electric to be]

There is nothing random here. It is well described by a beautiful relativistically invariant theory. You might have to learn more about how it works and how it is described before you can appreciate it though.

I suppose so. I'm an EE major but I love physics and I'm scared I won't be able to cover this kind of things during undergrad. Is this type of thing (tensor math) covered in a special relativity EM undergrad class?

 

[Orodruin]

I suppose so. I'm an EE major but I love physics and I'm scared I won't be able to cover this kind of things during undergrad. Is this type of thing (tensor math) covered in a special relativity EM undergrad class?

You are likely to use Maxwell's equations and the retarded potential to deduce the field of a moving charge rather than Lorentz transforming a stationary field in introductory courses. I might be wrong though, it is going to differ between universities.

 

[Electric to be]

You are likely to use Maxwell's equations and the retarded potential to deduce the field of a moving charge rather than Lorentz transforming a stationary field in introductory courses. I might be wrong though, it is going to differ between universities.

Now one last question, if people could always deduce that fields of charges change with velocity and frames using maxwells equations, then how did they define what q*E was equal to? Force? And then, what was force equal to? Ma? But acceleration is different from frame to frame right? How could you even describe what it meant to have different field magnitudes in different reference frames before relativity?

 

[Electric to be]

I guess what I'm asking is how do fields relate to forces in relativity? Is a F = qE + qv x B no matter what, but it is the Force which changes definition?

 

[tech99]

Now one last question, if people could always deduce that fields of charges change with velocity and frames using maxwells equations, then how did they define what q*E was equal to? Force? And then, what was force equal to? Ma? But acceleration is different from frame to frame right? How could you even describe what it meant to have different field magnitudes in different reference frames before relativity?

As a matter of interest, it seems that James Clerk Maxwell was aware of the issues surrounding frames of reference and fields, and it is thought he was on the verge of discovering relativity when he died.

 

[Electric to be]

As a matter of interest, it seems that James Clerk Maxwell was aware of the issues surrounding frames of reference and fields, and it is thought he was on the verge of discovering relativity when he died.

I just don't get how there can be a framework for transforming fields before relativity. If a field was defined to be essentially, ma/q = E. With the transformation of a field certainly has to come with the transformation of the definition of force though?

 

[Orodruin]

This was a known issue and one of the key ingredients when Einstein developed relativity. Maxwell's equations are not compatible with classical mechanics so the short answer is that there was no notion of field transformations before relativity.

(It was known that Maxwell's equations were invariant under Lorentz transformations, but Einstein made the important physical connection. After all, they are called Lorentz transformations and not a Einstein transformations.)