If charged particles that are stationary are electric, those that move uniformly are magnetic, and those that accelerate emit radiation, what happens with those that jerk or snap?
Jerk and snap being the first and second derivatives of acceleration with respect to time.
I don't know how to categorize this post on my mobile phone. It's physics obviously
Posted Sep 4, 2016, 5:27 PM UTC
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To clarify, a charged particle always produces an electric field. If it's moving, it produces a magnetic field as well.
Then the radiated intensity changes with time.
The potentials due to an electric charge moving arbitrarily are the Lienard-Wiechert potentials.
From these you derive the Larmor formula. The nonrelativistic version says that the radiated power depends only on the acceleration, not any higher derivatives of the velocity. The relativistic version says that it depends on the velocity and the acceleration, but still no higher derivatives.
If the particle has a nonzero jerk, snap, etc., then the acceleration is a function of time.
this universe is weird
And still want to know what jerk and snap mean...
The derivatives of position with respect to time are called velocity, acceleration, jerk, snap, crackle, and pop. Seriously.
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Can our bodies feel or detect snap, crackle, and pop ?
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Jerk is the rate of change of acceleration with time. Snap is the rate of change of the jerk. Then there's crackle, then pop, etc.
As a chemist with no experience in the field... Obviously I understand the meaning of these derivatives, but what applications do they have? Is there a limit wherein further derivatives are "impossible"? Is it limited by dimension or some other physics I know nothing about?
Velocity is a measure of how quickly position changes over time.
Acceleration is a measure of how quickly velocity increases or decreases over time.
Jerk is a measure of how quickly acceleration increases or decreases over time.
Snap is a measure of how quickly jerk increases or decreases over time.
Was there a reason you used "changes" for velocity and not the others?
Imagine you're driving along in a car and the speed limit changes from 55 to 70 so the driver starts accelerating, as they're on their way to 70 they tap the brakes--that is jerk. Snap, crackle, and pop... not sure what that feels like :).
you just need to come up with strange analogies. like someone emptying water bottles from a moving train at an increasing rate while the driver oscillates the gas pedal. you can be dam sure youre gonna get some snappy crackles then
Acceleration is a change of direction too, so presumably if you wiggle a steering wheel you're going to experience some of these things.
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Jerk - you know when you are coming to a stop in your car and slowly let go of the break over the last few feet and it's a smooth stop vs. keeping your foot down on the break so that the car comes to a stop and you jerk forward (sorry for the play on words, but that's a mnemonic for this)? The first is an example of applying a smaller and smaller force on the car to stop it over the last few feet, meaning deceleration was getting smaller over time, so there was a continuous change in acceleration (jerk is small). In the second situation deceleration is constant the entire time you are breaking and then when you stop acceleration abruptly stops (jerk is large). You experience jerk every day.
Snap is the change in jerk over time. I'm sure there's an everyday example for this, even in the above scenario but it might get convoluted. From what I understand, rockets lifting up into space experience a lot of jerk and this in turn means that snap becomes significant. Something about mechanical stress over time of the rocket.
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How can a charged particle ever not be moving? Wouldn't wave-particle duality mean that a particle could always be considered "moving" to some extent?
Having a wavelength doesn't mean that a particle is moving. It is perfectly possible for a charged particle to be stationary with respect to some reference point.
That makes sense but now I'm confused. Would that mean that something stationary in one reference frame that wasn't producing a magnetic field, would be producing a magnetic field in another?
E.G. if I have a "stationary" electron here on earth, and I don't observe a magnetic field. However, if you consider it as it hurtles through space on a giant rock, would it be producing one?
I guess the heart of my question is, is it always "producing" a magnetic field? Is it just that the field is effectively null when it is stationary in a given reference frame?
Yes.
Yes (ignoring its intrinsic magnetic dipole moment).
Absolutely. In fact, this is a good way to derive the existence of magnetic fields from electric fields and relativity. Of course, the actual historical derivation got relativity out of E&M.
I believe Spacetime Physics, by Taylor and Wheeler go through this case.
Magnetic fields are basically what electric fields look like in other reference frames. Since the frame determines whether you see an electric or magnetic field, it's really the electromagnetic field that exists and we see different aspects of it in different situations.
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That's exactly what we said when we theorized the black hole, antimatter, and the Higgs boson, to name a few. The field is called "theoretical physics", not "engineering". We have to respect and inspect the results whether or not we think they're readily applicable today.
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The answer given is a classical (i.e. not quantum) explanation, and so of course it doesn't account for quantum mechanical effects.
I would not say that "wave-particle duality" means that a particle will always be practically considered to be in motion; the Heisenberg uncertainty principle is the reason for that. The better you know a particle's position, the less well you know its momentum and vice versa. That is not the same as wave-particle duality!
And the effect that this has is that any real, unbound electric charge is going to radiate a little bit in practice. This is, ultimately, the source of blackbody radiation. Particles in an object are constantly jigging around; the hotter the material, the more they jiggle, and jiggling charges radiate!
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How can we tell if a particle is moving if relativity asserts that it's impossible to tell? And how can we tell if the particle is accelerating or just in a gravitational field?
Never studied any phsyics, but reading the question, I thought exactly this. Not surprising, in fact it would be weird if it was anything else.
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