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The addition of infinitesimally small parallel electric and magnetc fields, irrespective of their origin or source, or physical feasibilty; seems to produce a seemingly impossibly large force. Or at least, the result does not sit well with me. It seems too big, but I cannot nail down anything wrong with it from a logical perspective.

Hence, in the Lorentz force equation, is there a limit to how small a electric/magnetic field can be, practicality aside?

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  • $\begingroup$ I'm not sure I understand this question. Why doesn't the Lorentz force equation sit well with you? Can you provide an example calculation that you feel like is implausible? $\endgroup$
    – J. Murray
    Commented Sep 27, 2021 at 0:59
  • $\begingroup$ Why would the addition of infinitesimal quantities have to produce something that is "impossibly large"? Have you ever studied integration in calculus? $\endgroup$ Commented Sep 27, 2021 at 3:30

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In this case, your intuition is simply incorrect. Maxwell’s equations are linear, so the field of some overall charge distribution is simply the sum of all of the fields of each little part.

However, there is one thing that may help. In your question you used the word infinitesimal. Classically we do treat charge as a continuum, so mathematically we do get an infinite number of infinitesimal charges.

However, that is just an approximation. Charge comes in a finite smallest unit. So the charge is always finite as is the field. So it is not an infinite sum of infinitesimal charges but rather a finite sum of finite charges.

The approximation is still useful, but if it helps you feel more comfortable then remember that it is an approximation.

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