L10 : Dielectric & Polarization - Capacitor & Capacitance, Physics, Class 12 Video Lecture - Class 12 | Best Video for Class 12

hello friends this video on capacitors
and capacitance part 10 is brought to
you by exam few calm no more fear from
exam please make sure that you have
watched all the videos till part 9
before going ahead with part 10 so now
that we have understood how does a
dielectric become polarized let us try
to explain you what is polarization how
do we define polarization as a quantity
so what did we see when electric field
is applied the positive and the negative
charges slightly get separated from each
other right not the positive and
negative charges rather the center of
positive charge and the center of
negative charge gets slightly displaced
or gets slightly away from each other so
do you remember I talked about dipole
what was dipole dipole was nothing but a
positive charge a negative charge
separated by a small distance right so
you can say that dipoles several died
tools are formed in a dielectric in
presence of electric field right now
whenever dipoles will be formed there
will be dipole moment associated with
that so we say that a dielectric
develops a net dipole moment in presence
of external electric field whether it is
polar or nonpolar doesn't matter but for
both of them what happens all the
negative charges come towards this end
all the positive charges accumulate
towards right so we can see that each of
these we act as a dipole so all of them
has some dipole moment so we can say for
the entire dielectric as a whole there
is a net dipole moment that is developed
right so this dipole moment per unit
volume is known as polarization so this
is how we define polarization so when
the electric field is applied to a
dielectric the Centers of positive and
negative charges get separated from each
other and the net dipole moment is
developed so this dipole moment per unit
volume is
as polarization polarization is denoted
by a capital P and this polarization is
directly proportional to the electric
field that means as the electric field
increases polarization also increases so
this is converted this proportionality
is converted into an equality
introducing a new constant that is Chi e
which is known as electric
susceptibility so this is again a new
term so electric susceptibility is
basically constant for a particular
dielectric so it balance from material
to material it basically tells us how
polarization values with electric field
right so this is what your polarization
is so a polarized dielectric is
equivalent to two charged surfaces with
induced surface charge densities Sigma P
and minus Sigma P C if you look at this
what do you see all the negative charges
tend to accumulate towards left and all
the positive charges tend to accumulate
towards right so we can say that this
dielectric this polarized dielectric is
equivalent to two surfaces such that one
surface has charged minus Sigma P and
this surface has charge plus Sigma P
right we can say this I hope it is clear
to you okay so let me quickly remind
what review whatever I told till now a
dielectric can be a polar dielectric can
be a non polar dielectric but as soon as
an electric field is applied the Centers
of positive and negative charges get
slightly separated from each other as a
result a net dipole moment is developed
this dipole moment per unit volume is
known as polarization polarization is
directly proportional to electric field
as electric field increases the
polarization also increases so a
polarized dielectric is considered
equivalent to two surfaces with charges
minus Sigma P
plus Sigma P right so this is all we
studied so far now I will introduce or I
will talk about to go terms one is
electric susceptibility which I I have
already introduced and the other one is
dielectric constant because they left a
constant is something which you will be
used when we will relate dielectrics
with your capacitors right so let us
look at it so now let us look at it
mathematically now let us suppose this
external electric field is e naught okay
so e naught as the external electric
field now because of this separation of
charges there will be an electric field
which will set up inside the dielectric
that is the induced electric field let
us call it as ep that is the electric
field due to polarization so what is the
net electric field net electric field e
will be equal to e naught minus EP
because EP is in the opposite direction
electric field will always be from
positive towards negative right so this
will be the reduced value of electric
field so basically we call this electric
field as reduced electric field right
now this EP that is the electric field
due to polarization what is this
electric field just now I told you that
this polarized dielectric can be
considered as equivalent to two surfaces
with surface charge density Sigma P
right so the electric field on a surface
is given by Sigma by epsilon naught we
already know that so we can write EP as
Sigma P divided by epsilon naught right
now what is Sigma P it is nothing but
charge per unit area let us suppose the
charge on this surface is Q or we say it
as Q P that is the charge beautifuler
ization so Q P divided by a if a is the
area of the surface right so this can be
written as this is rather written as P
I did by epsilon not so that means this
quantity charge per unit area is termed
as polarization right so from this what
do we see now you must be wondering how
did I directly write this charge per
unit area as polarization if you
remember the definition of polarization
what is polarization it is dipole moment
per unit volume right so what is dipole
moment dipole moment is nothing but
magnitude of each charge that is Q into
the distance between them let us suppose
if the distance between them is a this
divided by volume now this distance if
you divide volume by this distance what
will you get area so you can see that
this is equal to charge per unit area so
dipole moment per unit volume is
equivalent to charge per unit area so
charge per unit area can be written as
polarization so P divided by epsilon
naught now I want to introduce what am I
trying to do are you able to guess I am
trying to introduce this constant that
is dielectric constant dielectric
constant is basically a constant which
is a characteristic of a particular
dielectric so it is different for
different dielectrics so a dielectric
constant characterizes a particular
dielectric right so here our dielectric
constant that is he is defined as the
ratio of the applied electric field to
the reduced electric field so E is the
reduced electric field and he not was
the original applied electric field so
the ratio of these 2 is nothing but
dielectric constant now dielectric
constant for a particular material is
always constant so this K is constant
for a particular material but it varies
from one material to another so it
becomes a characteristic of a particular
material so dielectric constant tells us
the ratio of the original electric
that is applied to the reduced electric
field so the electric field which gets
reduced due to the presence of the
dielectric right so this is our
dielectric constant now let us talk
about electric susceptibility electric
susceptibility is denoted by Chi E as I
told you before also that polarization P
is always directly proportional to the
electric field E so we can see that so
this polarization was equated with a
constant Chi e with electric field later
if Simon naught was also introduced so
that Chi E can be kept dimensionless I
mean to make this equation dimensionally
balanced on both sides epsilon naught
was introduced so that guy can stay
dimensionless so Chi is a dimensionless
quantity Chi tells us the ratio of that
as electric susceptibility tells us the
ratio of polarization to that electric
field that is how this polarization
varying with electric field so electric
susceptibility basically describes the
electric behavior of a dielectric as I
told you dialing now are you
understanding what is the purpose of a
dielectric dielectrics are non
conducting substances they do not
conduct electricity but they show some
electric behavior as you can see here
even though they do not conduct
electricity but still when electric
field is applied and electric field is
set up inside the dielectric that is a
reduced electric field stays inside the
dielectric so there is electric behavior
which is seen inside the dielectric so
that electric behavior is determined by
this quantity that is electric
susceptibility because it tells us how
the molecule how the dielectric getting
is getting polarized with that electric
field right so I hope you have
understood these two terms properly
dielectric constant and electric
susceptibility now I will establish a
relationship between dielectric constant
and electric susceptibility in our
previous slide we saw that the reduced
electric field is equal to the applied
electric field minus the polarized
electric field or the electric field
which arises
- polarization so this we can write it
he not - EP what was polarized electric
field we saw that polarized electric
field was equal to polarization divided
by epsilon not in I've in my previous
slide I proved how this is equal to this
now again we can write polarization as
epsilon naught into KY into e this
divided by epsilon naught I am sorry
this - so E is equal to this now this
epsilon naught and epsilon not gets
cancelled so let us bring all the YZ
together so E + KY e becomes equal to e
naught right so here we say 1 plus KY
into E is equal to e naught again we can
say e naught divided by E is equal to 1
plus KY what is e naught divided by e
that is the original electric field
divided by the reduced electric field
what is this it is nothing but the
dielectric constant that is K so
dielectric constant is equal to 1 plus
the susceptibility of the dielectric so
this is the relationship between
dielectric constant and electric
susceptibility clear so this is an
important relationship so it is better
if you remember this thank you please
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