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Therefore, the volume of the conductor = Al
If n is the number of free electrons per unit volume of the conductor, then the total number of free electrons in the conductor=A/n.
If e is the charge on each electron then total charge on all the free electrons in the conductor
Q=A/ne (1)
Let a constant potential differences V is applied across the ends of the conductor with the help of a battery
The electric field set up across the conductor is given by
E=V/l
Due to this field, the free electrons present in the conductor will begin to move with a drift velocity vdtowards the left hand side of the conductor.
Thus the time taken by the free electrons to cross the conductor is
t=l/vd (2)
As current I=q/t (3)
By substituting equation (1) and (2) in equation (3),
We get
I=Alne/l/vd
Or I=Anevd (4)
Since A,n and e are constant
I∞vd
Hence the current flowing through a conductor is directly proportional to the drift velocity.
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