Energy of EM Waves Video Lecture | Physics for JEE Main & Advanced

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electromagnetic waves part 6 is brought
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from exam please make sure that you have
watched all the videos to the part 5
before going ahead with part 6 now let
us look at the energy in an
electromagnetic wave now let us see I
mean okay fine
so till now we understood that if we
have an electric field that the magnetic
fields and if they are time varying and
coupling they give rise to
electromagnetic waves but what is the
purpose of electromagnetic waves I mean
what purpose do they serve do they carry
energy with them yes of course
electromagnetic waves as the wave
propagates energy gets scattered and
this is the most important property
because of which the electromagnetic
waves have so much of practical
applications I mean for anyway for that
matter if a wave doesn't carry energy I
mean I don't think it can they put up
into many practical purposes so carrying
energy is one of the basic property of
waves because of which they are so much
helpful in our day to day life so now in
this slide we will see how much energy
is carried by an electromagnetic wave
energy in an electromagnetic wave is
partly carried by electric field and
partly by magnetic field because
whenever we talk about electromagnetic
wave electric field and magnetic field
both play equally important role right
so when I talk about the amount of
energy that has been carried by an
electromagnetic wave that is also
divided between both of them half of the
energy gets carried by electric field
some of the energy gets carried by
magnetic field so now let us look at it
mathematically now we already we know
that let us try to calculate the energy
stored per unit volume in an
electromagnetic wave so what will be the
energy stored per unit volume let us
denote it as e P that is the total
energy stored per unit volume in an
electromagnetic
so this total energy will be equal to
the energy stored per unit volume by
electric field plus the energy stored
per unit volume by magnetic field now we
have already seen in our lessons on
electricity that energy stored per unit
volume is given by half epsilon naught T
square right we have already derived all
these expressions that energy stored per
unit volume by an electric field is half
epsilon knot e square and then I'll
choose toward per unit volume by
magnetic field is half v square divided
by nu mod right so the total energy
stored per unit volume in an
electromagnetic wave is this Plus this
right now we also know that the velocity
of an electromagnetic wave it was
experimentally found we will talk about
it when we discuss the properties of an
electromagnetic wave the speed of an
electromagnetic wave speed of
electromagnetic wave is equal to the
speed of light that is C and this speed
is equal to the ratio of the electric
field and a magnetic field so C is equal
to e by B so this was experimentally
found that speed of an electromagnetic
wave is the same as the speed of light
and that is equal to the ratio of
electric field to the magnetic field now
using this we can write that e total is
equal to half epsilon knot e square plus
half into instead of B we can write it
as e divided by C so B Square will be e
square divided by C square into mu knot
right we also know that from Maxwell's
equations if you saw that it
experimentally it was also found that
the speed of light C is equal to 1
divided by root over mu naught epsilon
not so using this we can say that 'total
is equal to half epsilon knot e square
plus half
a square divided by mu naught into 1 by
C square that means mu naught square
epsilon naught square ok this is e
square divided by C square C square
would be mu for C square would be mu
naught epsilon naught right so this mu
naught mu naught will get cancelled so
this is equal to half epsilon naught E
square plus half epsilon naught E square
so this is equal to epsilon naught e
square therefore the total energy stored
per unit volume in an electromagnetic
wave is given by epsilon naught e square
and this is the amount of energy per
unit volume that will get carried by the
electromagnetic wave so half of this
energy is guided by electric field and
the remaining half of the energy is
scattered by the magnetic field so as
the wave propagates the energy gets
carried from one place to another so
this is the energy which gets carried
away by the electromagnetic wave
now since the electromagnetic wave
carries energy therefore it has so many
practical applications in communication
systems now we will talk about thank you
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