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I do not get why current density of electron in Bohr orbit is $\vec j = e\vec v$, where $e$ is the electron charge and $\vec v$ is the velocity of the electron.

I know that current is $I = ev/(2\pi r)$ where $r$ is the radius of the orbit. How can $\vec j$ be derived from here?

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    $\begingroup$ From the way you write $I$, one would assume that $e$ has units of charge in your expressions. That would imply that your expression for $j$ has units of charge$\times$lenght/time. But current density usually has units of charge/(length$^2\times$time). Aren't you missing a delta function in the expression for $j$? $\endgroup$
    – secavara
    Commented Feb 11, 2018 at 23:09

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The expression $j=ev$, $e$ electronic charge, $v$ velocity, cannot be a current density, i.e., charge per time and per area. The dimension is charge times length per time. Charge per time is a current, thus it is current times length not per area.

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