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If $f=ma$, then why is the formula for calculating the force due to a electromagnetic field on a charged particle (Lorentz force law), ${\vec{F}}=q{\vec{E}}+q{\vec{v}}\times {\vec{B}} $, totally independent of mass?

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  • $\begingroup$ I edited the vector symbols. For the future: use e.g. \vec{F} $\endgroup$
    – paleonix
    Apr 15, 2020 at 12:29

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You are mixing up the two sides of the equation. $\vec{F}=m\vec{a}$ is more general, it describes how any force acts on an object of mass $m$, while the Lorentz force law describes one special force. So if you want to know the acceleration you equation becomes $$ m\vec{a} = q \vec{E} + q \vec{v} \times \vec{B} $$ The reason you are misunderstanding it is probably that you are used to classical mechanics where most of the time your force is the gravitational force which is again proportional to the mass. But if you think of Hooke's law for the force coming from a spring, it is also not proportional to the mass.

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    $\begingroup$ If some forces are independent on mass then why is f=ma a universal equation. Is it that f=ma does not describe the force occurring here but actually describes what the effect of the force will be on a mass? $\endgroup$
    – user248823
    Apr 15, 2020 at 12:34
  • $\begingroup$ Exactly. It doesn't describe the force, but how any force acts on a mass. $\endgroup$
    – paleonix
    Apr 15, 2020 at 12:48

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