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The mobile charged particles within a conductor move constantly in random directions, like the particles of a gas.
In order for there to be a net flow of charge, the particles must also move together with an average drift rate.
Electrons are the charge carriers in metals and they follow an erratic path, bouncing from atom to atom, but generally drifting in the opposite direction of the electric field.
The speed at which they drift can be calculated from the equation:

2.064 seconds.