- #1

Researcher720

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As I understand it, the current density function can be written as

$$ \vec{J} = \rho \vec{v}_S$$

where ρ is the charge density function and v_S is the continuous source charge velocity function. What I am confused about is why there isn't another part involving the test charge (or detector, or observation point) velocity? For example

$$\vec{J} = \rho ( \vec{v}_S - \vec{v}_T)$$

where v_T is the test charge (or detector or observation point) velocity in the arbitrary coordinate system chosen.

If you have a test charge, and source charges, since you can't tell if the source charges are moving with a constant velocity versus the test charges moving in the opposite direction at constant velocity, it seems that the current density J should involve the difference of these two independently moving objects (test and sources). What am I missing?