bei48482_FM

352 Chapter Ten

After each collision, the electron is accelerated for some time interval tbefore the

next collision, and at the end of the interval has traveled^12 at^2. When the electron

has made many collisions, its average displacement will be X^12 at^2 , where t^2 is

the average of the squared time intervals. Because of the way tvaries, t^2  2 ^2.

Hence Xa^2 and the drift velocity is Xa, so that

Drift velocity da (10.12)

In Example 10.2 we found that the current Iin a conductor of cross-sectional area

Ain which the free electron density is nis given by

InAed (10.13)

Using the value of dfrom Eq. (10.12) gives

I

Since the electric field in the conductor is EVL,

IV (10.14)

This formula becomes Ohm’s law if we set

R (10.15)

The quantity in parentheses is known as the resistivityof the metal and is a con-

stant for a given sample at a given temperature:

Resistivity  (10.16)

mF



ne^2 

L



A

mF



ne^2 

Resistance of metal

conductor

A



L

ne^2 



mF

nAe^2 E



mF

eE



mF





F

eE



m

E

Figure 10.17An electric field produces a general drift superimposed on the random motion of a free

electron. The electron’s path between collisions is actually slightly curved because of the acceleration

due to the field.

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