Can anyone refer me to a discussion of applying the technique of changing reference frames to problem solving? Why it works, and what it means. I'm familiar with using it in some E&M problems, but I guess I don't really "get" it. For example a particle in an E&M field has(adsbygoogle = window.adsbygoogle || []).push({});

[itex] m\vec{a} = q(\vec{E}+\vec{v}\times\vec{B})[/itex]

It's common to set [itex]\vec{v} = \frac{\vec{E}\times\vec{B}}{B^{2}} + \vec{u}[/itex] to "cancel" the [itex]\vec{E}[/itex] field and just work out the circular motion for the magnetic field.

What does this say about the physics of the system? Is it right to say the particlereally(in the original frame) is moving in a circle "plus" the velocity of the frame? That is, if I want the velocity, I find it in the intertial frame, then just tack on the [itex]\frac{\vec{E}\times\vec{B}}{B^{2}}[/itex] term?

That's right answer, but can someone point me to some formal proof for the general case of any moving particle? I've never seen it stated in general, it's always just the professor going "oh, let's wave our hands like this and make [itex]\vec{E}[/itex] go away..." during an example problem. I use it, but I've never reallylearnedit, so I always have trouble explaining this. I usually say something like "if you add a constant to the velocity, it won't change the [itex]\frac{d\vec{v}}{dt}[/itex]"

Or maybe if you've taught a class before, how did you explain it to your students?

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# The inertial frame trick.

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