let us study about drift velocity of free
electrons. we have discussed that in the situation
of conductor when, a battery is connected
across it. and, the circuit is closed. You
can just have a look on the situation i am
drawing here. this a battery which is connected
across cylindrical conductors wire switch.
as soon as the battery is closed this positive
terminal of battery and negative terminal
of the battery. we’ll apply a potential
difference across the terminals. say on a
negative side we consider zero potential then
on the positive side potential will be v volt
higher then the negative terminal. so their
exist a potential difference. and from high
potential to low potential an electric field,
e is established in the conductor. due to
which the free electrons in the conductor
will experience a force in leftward direction.
here if the switch was open. in that situation
we can say that every free electron, would
be in random motion, they will behave just
like gas molecules in container. and would
be in brownian motion like this. but as soon
as the switch is closed. an electric field
is established, and every electron will experience
a force, e-e. in the direction opposite to
the electric field. due to which these electrons
have a tendency to move toward left and all
these electrons will start moving toward left.
and certainly due to their random motion they
can not move in a straight line they will
move in. a random zigzag path toward left
because continuously during motion these are
also colliding with the, neighboring electrons.
so we can say over all drift of electrons
will exist in leftward direction, but these
will not move straight. so in this situation
we can say due to continues collisions with
neighboring electrons. each electron we can
say. will experience a force. for the drift,
due to the electric field e-e. and we’ll
also experience a force which is the opposing
force due to continues collision on electrons
opposite to the direction of their motion.
the speed of electron is v. due to continuous
collisions the net friction the electron will
experience can be written as k v which is
directly proportional to the speed. so in
this situation, if we find out the acceleration
of electrons, acceleration of free electrons.
can be written as e-e minus k v by m. and
here you can say due to acceleration the speed
of electrons will increase. and as electron
speed increases this opposing force increases
because the rate of collision increases with
the speed of electrons. so this k v is increasing
that will reduce the acceleration, and at
some maximum speed this acceleration become
zero we can say this will be equal to zero
when. the speeds become e-e by k, here k is
just proportionality constant which depends
on lattice parameter of the. material in which
the electrons are flowing. so here we can
see this is the speed which electrons will
attain when acceleration become zero that
means, these electrons will. further move
with this constant speed. and here you can
see this speed is directly proportional to
the applied electric field. this can be written
as mu e. where mu is another constant, which
is, the ratio of electron charge and. constant
k which we have used in. finding the opposing
force on electron due to collisions. now this
is the speed we write as v-d or this is called.
drift speed of electrons. in. current carrying
conductor. so this is the speed. with which
electrons will continuously flow, on an average.
and it’ll remain constant. and it’ll constitute
the constant current in the circuit. that’s
why we say on applying the battery potential
difference when electric field is setup. electrons
free electrons in the conductor will not.
continuously accelerate. these will not continuously
accelerate these will accelerate for a short
time and finally attain a drift speed, when
the electric force and the, force due to continuous
collision and electrons with the neighbors
get balanced. so that is the speed with which
in a current carrying conductor free electrons
travel this proportional to, the electric
field and here the proportionality constant
mu. we termed as. mobility of. free electrons.
in the metal. depends on. lattice parameters
of the metal as well as it depends on the
temperature, if we increase the temperature
certainly rate of collision increases due
to more randomness and mobility will decrease.
that also we’ll discuss.
