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Derive the relationship between current in conductor and drift velocityin terms of number of free electrons per unit volume of conductor.

Derive the relationship between current in conductor and drift velocityin terms of number of free electrons  per unit volume of conductor.

Grade:12

1 Answers

Arun
25763 Points
4 years ago
Let l is the length of the conductor and A uniforms area of cross-section.
 

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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