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Physics
Classical Physics
Electromagnetism
What is the origin of Lorenz force?
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[QUOTE="vanhees71, post: 6579994, member: 260864"] One should first emphasize that it's Lorentz force and not Lorenz force. It goes back to the Dutch physicist Hendrik Antoon Lorentz, who discovered "classical electron theory", i.e., he started the modern understanding of electromagnetic phenomena as the interaction of charged particles ("electrons") with the electromagnetic field. One should also emphasize that there is one Lorentz force, which is (in SI units) $$\frac{\mathrm{d} \vec{p}}{\mathrm{d} t}=\vec{F}=q (\vec{E}+\vec{v} \times \vec{B}). \qquad (*)$$ In manifest covariant form the equation of motion for a charged particle in an electromagnetic field (neglecting the notorious problem of "radiation reaction") is given in #5. Note that these equations can be split in temporal and spatial components as $$\frac{\mathrm{d} p^0}{\mathrm{d} \tau}=q \vec{E} \cdot \vec{u}, \quad \frac{\mathrm{d} \vec{p}}{\mathrm{d} \vec{\tau}}=q (u^0 \vec{E}+\vec{u} \times \vec{B})=\frac{q}{\sqrt{1-\beta^2}} (\vec{E}+\vec{v} \times \vec{B}),$$ where ##\beta=|\vec{v}|/c## and ##\gamma=1/\sqrt{1-\beta^2}##. Multiplying the latter equation by ##1/\gamma## leads to (*). One should note that $$p^{\mu}=m u^{\mu}=m \frac{\mathrm{d} x^{\mu}}{\mathrm{d} \tau}$$ is a four-vector with the proper time of the particle defined by ##\mathrm{d} \tau=\mathrm{d} t \sqrt{1-\beta^2}##. Ludwik Lorenz was a Danish physicist. The similarity of their names is indeed confusing and sometimes to the disadvantage of Lorenz, who nowadays is rightfully credited as the discoverer of the advantage of the Lorenz gauge. In many older textbooks they called it "Lorentz gauge", but Lorentz used it some years later than Lorenz, and so it's more to the historical facts to call it Lorenz gauge. The name of both phycists occurs in the theory of dielectrics in the socalled "Lorentz-Lorenz formula". [/QUOTE]
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What is the origin of Lorenz force?
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