4
$\begingroup$

We know that the magnetic force on a particle moving in a magnetic field was found by J.J. Thomson in 1881, with a slight mistake, and then corrected by Heaviside in 1885 to $F_M = q\,v\times B$.

Can you tell me when was discovered that its ratio to the electric force was $v^2/c^2$, and how was it determined? I suppose it could have been done only in a cyclotron.

Then, lastly, do you know when and who decided that $F_M$ was just $F_E$ seen in a different system exploiting the resemblance of the ratio with a Lorentz transformation, unifying the two forces ?

$\endgroup$
4
  • $\begingroup$ Hi, we prefer one question per post. Your second question probably has a rather long answer, so it would be easier to deal with in a separate post. $\endgroup$ Oct 18, 2019 at 13:21
  • $\begingroup$ I am not sure what ratio you are referring to. Lorentz derived the formula for the total force exerted by the electromagnetic field on a moving charged particle, now called the Lorentz force, as $F=q\,E+q\,v\times B$ in 1895. He did not need a cyclotron, only Maxwell's equations. But the ratio of the components does not need to be $v^2/c^2$. $\endgroup$
    – Conifold
    Oct 19, 2019 at 4:51
  • 1
    $\begingroup$ @Conifold, lorentz has nothing to do with my question. He simply joined in one formula the electric and magnetic force acting on a charge. My question is about the ratio between the two forces (FM)/E. Two electrons circling a ciclotron at C/2 feel two forces E, repulsive, and M, attractive, which is 1/4 of E $\endgroup$
    – user157860
    Oct 19, 2019 at 12:04
  • 1
    $\begingroup$ @CarlWitthoft, it is one question because who joined the forces did it because of the resemblance of v^2/C^2 with relativity transformation $\endgroup$
    – user157860
    Oct 19, 2019 at 12:06

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.