Saturday, 25 July 2020

Magnetic force between two charged particles?


I know the gravitational force between two particles with masses $m_1$, $m_2$:



$$ \vec{F} = \frac{Gm_1m_2}{|\vec{r}|^2} \hat{r} $$


And I know the electrical force between two particles with charges $q_1$, $q_2$:


$$ \vec{F} = -\frac{Kq_1q_2}{|\vec{r}|^2} \hat{r} $$


($\vec{r}$ is the position vector of particle 2 from the referential of particle 1 and $\hat{r} = \frac{\vec{r}}{|\vec{r}|}$)


I've been looking for an expression like these for the magnetic force since 2012... Then I found Physics Stack Exchange. Does anybody know if such formula exists?




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