The force on one charged particle due to a uniform magnetic field is $F=qvB\sin\theta$. According to this formula, the faster the particle's velocity, the greater the force of the magnetic field is going to exert on the particle. However, how does the magnetic field know how fast the particle is moving?
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2$\begingroup$ What does it mean for the field to "know" how fast the particle is moving? $\endgroup$– ACuriousMind ♦Jul 26, 2019 at 9:52
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$\begingroup$ I only mean that why is the force on a charged particle created by the magnetic field have to do with the velocity of the particle? Why is it not a constant given that the charge and the magnetic field is constant? Sorry if this question seems too elementary, because I am just starting to learn about electromagnetism. $\endgroup$– Michael WangJul 26, 2019 at 21:43
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$\begingroup$ @MichaelWang The interaction of charged particles with magnetic fields is basically an interaction of magnetic moments and fields. A moving charged particle has a field in the reference frames in which it is not at rest. The strength of that field depends on how fast it's moving. That field interacts with the static field. E&M gets "weird" when you include special relativity because there are frames in which magnetic fields can become zero. $\endgroup$– Bill NJul 28, 2019 at 13:48
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$\begingroup$ How is the question unclear? $\endgroup$– Michael WangJul 28, 2019 at 18:12
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2 Answers
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Fields don't "know" anything. "Knowing" is a anthropomorphic concept, based around how humans believe they operate.
The effects of a magnetic field on a charged particle are proportional to the derivative of position with respect to time. This is simply the equation used to predict the effects a magnetic field has.
Perhaps even more interesting is the Coriolis effect. The Coriolis effect fields a pseudo-force which is a function of the velocity of a particle. This is true, even though the Coriolis effect is merely an effect of viewing the trajectory of a particle in a rotating reference frame -- there is nothing physical to which we could even attribute its effects.
answered Jul 26, 2019 at 6:44
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$\begingroup$ See also: Resemblance between Coriolis force and magnetic part of Lorentz force $\endgroup$– RuslanJul 26, 2019 at 9:58
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The closest argument to a reason why the magnetic force depends on the velocity is that, fundamentally, the the four potential $A^\mu = (V, A^x, A^y, A^z)$ is coupled to the charge current $j^\mu = (q, j^x, j^y, j^z)$, which depends on the velocity of the charges.
