How do magnetic fields due to random motions of charges cancel out in a current-carrying wire?

Question

In my physics textbook, it states that

magnetic fields due to random motions of charges cancel out at every point

I know there's a drift velocity due to force imposed by the electric field, but the random motions still persist as electron won't give them up. But how exact does the magnetic fields due to random motions cancel out at every point?

Dale · Accepted Answer

The source of the magnetic field is the current density $vec J$. Randomly moving charges have $vec J =0$ and therefore produce no magnetic field.

How do magnetic fields due to random motions of charges cancel out in a current-carrying wire?

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