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XII CLASS PHYSICS Unit 2 TOPIC PAGE 3

page 3



Drift velocity(vd) :every metal has a larger no of free electrons. they move randomly inside the metal about velocities 10^5m/s. however these velocities are destributed randomly in all directions.  there is no net direction of motion .so their average  velocity is zero. vectors(u1, u2, u3........ .. un)  are the randomly velocities of n free electrons then average velocities are
   

vectors(u1+u2+u3+... . +un) /n=o



hence their is no net flow of electron in any direction & no current flow.
when  a potential difference is applied across a conductor an electric field is set up at every point inside the conductor andeach electron experiences a force in the opposite direction of electric field and move with an acceleration. as the electrons accelerates they collide with a very small velocity(10^-5)  oppositeto electric field is called drift velocity hence drift velocity is the average velocity of the free electrons with which they are Drifted inside the conductor when a potential difference is applied across it.  it is denoted by vd

consider a conductor of length( l )& cross section area (a) . let a potential difference( V)  is applied across it .then an electric field (E)
is setup in the conductor
where E=V/l
and force on an electron

vector f=-e×vector E


then acceleration of an electron


  vector a= vector F/m=-e ×vectorE/m


where m is mass of an eletron .if electron accelerates for time t1 during collision b/w 1 electron & +ve ions.  then velocity of electron vector v1=vector u1+ vector a×t1


similarly v2=u2+a×t2

               v3=u3+a×t3
. . .. ... ... ...  .. 
. . .  .. ... vn=un+a×tn
  note(represent over vector sign)

then average velocity = (u1+a×t1+u2+a×t2+..  ..  .. .. .. .. .. . . .. . ...   .. .. .. ..   .un+a×tn) /n
          =(u1+u2.. ... un) /n +[a(t1+t2+.. .. tn) /n  =T]
          = 0+a×T


this average velocity is equal to drift velocity vd

put value of a from above

 we get vd=(-e×E×T) /T
 in magnitude vd=(e×E×T) /m


where T is average time b/w two successive collision

where T= (t1+t2+t3..... ... +tn) / n

this time is known as relaxation time and is the order of 10^-14s. it decreases with the increase in temperature .

Relaxation time :average time spend b/w two successive collision of electron with +ve ions is called relaxation time




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