Final answer:
Increasing the length of a copper wire while keeping the cross-sectional area the same would require an increase in voltage to maintain the same drift velocity, otherwise, the longer wire would have a reduced current and lower drift velocity.
Step-by-step explanation:
When a copper wire of length 'l' is replaced by another copper wire with the same cross-sectional area but of length '4l', the drift velocity will change due to the length of the wire affecting the resistance, which in turn affects the drift velocity. The drift velocity, vd, of charge carriers in a conductor, where the current, area, and charge are constant, is inversely related to the number of charge carriers per unit volume, 'n', according to the relation I = nqAvd. Since the material and cross-sectional area remain the same, 'n' and 'A' do not change. However, increasing the length of the wire increases its resistance by a factor of four, assuming resistivity and area are constant. According to Ohm's law, V = IR (where 'V' is voltage, 'I' is current, and 'R' is resistance), and since 'I' is constant, for the wire of length '4l', the voltage across it would need to increase by a factor of four to maintain the same current, thereby maintaining the same drift velocity. Without an increase in voltage, the longer wire would have a reduced current, and hence a lower drift velocity.