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I have seen in some texts that the Galilean transformation of the magnetic field across inertial reference frames is given by: $\vec B'= \vec B - (1/c^2)(\vec v\times \vec E)$. Every where it is stated that it can be derived using Galilean transformation. However I have never found it derived using only Galilean transform. (i.e. without taking help of Lorentz transformations). The other equation concerning Galilean transformation of electric field: $\vec E'=\vec E + (\vec v \times \vec B)$ has been seen derived by only Galilean transformation (i.e. by invariance of Lorentz force) very elegantly in many texts. Is it possible to derive this equation $\vec B'= \vec B - (1/c^2)(\vec v\times \vec E)$ by only using Galilean transformation?

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  • $\begingroup$ See related question: What is the Galilean transformation of the EM field? $\endgroup$ – Thomas Fritsch Jul 11 at 12:41
  • $\begingroup$ I have seen in some texts Please give titles and authors. This claim just sounds wrong to me. For a treatment of this topic, see Marc De Montigny, Germain Rousseaux, "On the electrodynamics of moving bodies at low velocities," arxiv.org/abs/physics/0512200 $\endgroup$ – Ben Crowell Jul 11 at 13:39
  • $\begingroup$ The subtlety is that the Galilean transform isn't unique; there are two different possibilities, in the so-called electric and magnetic limits. That's why, to avoid confusion, it's almost always best to start from the Lorentz transformations and take either limit. $\endgroup$ – knzhou Jul 11 at 14:42

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