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.