Charges moving parallel to magnetic fields and direction of magnetic force

[nateja]

I hope this isn't in the wrong forum, it's not a problem, just a conceptual question for physics 2.

I have a few questions that I cannot find answer for in my physics book or online.
1) Why does moving a charge parallel to the magnetic field result in zero magnetic force?
Is this quality based on experimental data like the magnetic force equation (something that the book mentions: says the mag-force equation was not developed theoretically, but experimentally)? F = qv x B. I know that due to the cross product, the force will just be 0, but is there another explanation besides just the math?

Why do opposite charges of equal magnitude result in different directions of magnetic forces? Is this a property of the electric fields from the oppositely charged masses (positive are isotropic and negative all point toward the negative charge)?

 

[tiny-tim]

hi nateja!

1) Why does moving a charge parallel to the magnetic field result in zero magnetic force? … I know that due to the cross product, the force will just be 0, but is there another explanation besides just the math?

here's a conceptual answer …

a velocity-dependent force is an inevitable consequence of relativity (good old-fashioned Newtonian relativity, not the einsteinian sort) …

imagine a stationary line of negative charge, and a negatively-charged particle moving perpendicularly towards it

obviously, it is repelled, so it slows down, is momentarily stationary, then speeds up again, moving away, all on the same perpendicular line

now look at it from a frame of reference in which the line is moving along itself at speed v …

what happens to the moving charge? ​

 

[nateja]

Thanks! my professor explained this in class with the same frame of reference example. Pretty cool stuff!