Timeline for Gyrating proton near magnetic pole of the Earth
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 24, 2023 at 19:42 | comment | added | AXensen | @gamma1954 It's very simple. I was wrong the second time. I've tried to fix the answer | |
| May 24, 2023 at 19:41 | history | edited | AXensen | CC BY-SA 4.0 |
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| May 24, 2023 at 19:38 | comment | added | gamma1954 | You mention "the fact that v⊥ (the velocity perpendicular to the magnetic field) is increasing when |B| increases". Alright, I understand why. But then you mention "a force in the θ^ direction, slowing down the particle" [in the direction perpendicular to the axis] and you mention "the particle loses perpindicular velocity". That's difficult for me to understand: the perpendicular speed increases and at the same time the particle loses perpendicular speed. Could you please explain this? | |
| May 24, 2023 at 9:58 | comment | added | AXensen | @gamma1954 it seems like there would be an easy way to prove conservation of angular momentum... but keep in mind it's only conserved in the adiabatic limit so it's not like you're going to find some simple relation that proves it's conserved. Also, normally when angular momentum is conserved it's because forces are never in the $\hat{\theta}$ direction... no such luck here that's exactly what I was calculating above - the effect of a $\hat{\theta}$ force. And finally, magnetic fields turn so the axis with which angular momentum is defined is changing with time which is odd. | |
| May 23, 2023 at 23:33 | comment | added | gamma1954 | Thank you, AXensen. Frankly, the invariance of the magnetic moment is only a "means to an end", it helps to prove that the gyroradius diminishes while the magnetic field gets stronger and the perpendicular component of the proton's speed increases. I now see my error of an increasing angular momentum corrected. If I can find a simple way to prove that the angular momentum is constant along the path, the decreasing gyroradius immediately follows from the increasing perpendicular speed. | |
| May 23, 2023 at 23:00 | history | edited | AXensen | CC BY-SA 4.0 |
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| May 23, 2023 at 22:54 | history | answered | AXensen | CC BY-SA 4.0 |