- #1
jjustinn
- 164
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Classical charged particle's reaction to a retarded field
This is something I've been curious about for a while -- every once in a while, I'll see some random reference to it in an article, but I never feel like it's the whole story.
The situation is this -- you have a moving classical charged object; for simplicity, say it's a point charge, but it works just as well for extended objects. We'll also say that its charge was 'turned on' at t = 0, and that it's moving along the positive X axis at a constant 1 m/s.
So, starting at t = 0, the charge is emitting electric / magnetic fields, according to the Maxwell equations. At t = 1s, the charge will be at x = 1m, but at that point, there is now a nonzero field from the charge t = 1 / c seconds prior, which is pointing in the positive X direction, so it would seem that the charge should be accelerating itself...so I feel like I'm missing something.
It doesn't seem like this should count as a self-field, since how would the charge know that it's "its field"? Another way to get around this excuse would be to say that the charge has a second point charge stuck an small distance in front of / behind it, that can also be 'turned on' at an arbitrary time, and we don't turn it on until t = 1s...so you get the same effect, but it's definitely not a "self-field" in any sense of the word.
So...what am I doing wrong here? My gut says that it's already worked into the Lorentz force / Maxwell equations, but I can't find that written anywhere.
Thanks -
Justin
This is something I've been curious about for a while -- every once in a while, I'll see some random reference to it in an article, but I never feel like it's the whole story.
The situation is this -- you have a moving classical charged object; for simplicity, say it's a point charge, but it works just as well for extended objects. We'll also say that its charge was 'turned on' at t = 0, and that it's moving along the positive X axis at a constant 1 m/s.
So, starting at t = 0, the charge is emitting electric / magnetic fields, according to the Maxwell equations. At t = 1s, the charge will be at x = 1m, but at that point, there is now a nonzero field from the charge t = 1 / c seconds prior, which is pointing in the positive X direction, so it would seem that the charge should be accelerating itself...so I feel like I'm missing something.
It doesn't seem like this should count as a self-field, since how would the charge know that it's "its field"? Another way to get around this excuse would be to say that the charge has a second point charge stuck an small distance in front of / behind it, that can also be 'turned on' at an arbitrary time, and we don't turn it on until t = 1s...so you get the same effect, but it's definitely not a "self-field" in any sense of the word.
So...what am I doing wrong here? My gut says that it's already worked into the Lorentz force / Maxwell equations, but I can't find that written anywhere.
Thanks -
Justin
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