In the previous nature we saw that e m waves
have any intensity which is equal to c times
average energy density u which is one half
epsilon zero e zero the amplitude square and
e m waves also carry momentum which is equal
to u percent unit area percent unit time and
as a result they can apply a pressure they
can carry a energy and give you heat now in
this lecture i am going to solve two examples
to give you an idea what the kind of electromagnetic
fields etcetera are related with electromagnetic
radiation coming out of of ordinary light
or also what kind of pressure to they apply
so this lecture essentially about numbers
as example one now let us take a sixty watt
bulb that means there light coming up out
is equivalent to power makes sixty watt and
calculate electric field amplitude and magnetic
field amplitude at a distance of one metre
form the bulb under the assumption assuming
that a bulb can be treated as a point source
i am taking this bulb to be a point sources
which is radiating isotopic radiating isotropically
that means there is no particular direction
in which radiates is prefer so what i have
is a bulk here which is giving out radiation
in all the direction and we want to see at
one meter what is the associated electric
field so all this electromagnetic waves of
propagating in the redial direction
let us look at one particular direction going
to the write electric field is going to be
perpendicular to that and source is going
to be magnetic field the power carried per
unit area and in this case is going to be
sixty jouls percent second divided by four
pi r square r we have taken to be one meter
so this is fifteen over pi watts percent meter
square that is the power and what is this
power percent unit area or energy percent
unit area percent unit time this is preciously
equal to the pointing vector and therefore
we have this c u which is c times half epsilon
zero e zero square is equal to fifteen over
pi and i want to calculate e zero e zero therefore
is going to be equal to thirty over pi t square
root
let's multiply is a calculation less multiply
by four multiply by four so this square root
of hundred and twenty over four pi c which
is equal to square root of hundred and twenty
times nine times ten raise to nine divided
by three times ten raise to eight this gives
me ten this gives me three so this is thirty
six hundred which gives me sixty volts percent
meter imagine this if you are standing one
meter form a sixty watt bulb at a distance
of one metre form it you have an electric
field related to that radiation coming out
of the balk sixty four percent meter over
one metre that is volt is difference is going
to be sixty four that is the how much the
electric field is
further away you go the power splits over
a larger area and therefore electric field
is going to go down how about the corresponding
magnetic field the magnetic field magnitude
is nothing but e zero over c so this is going
to be c over three time ten raise to eight
tesla which is twenty time ten raise to minus
eight which is two time ten raise to minus
seven tesla so associated magnetic field is
really very very small as example two 
i am going to talk about a laser pointer which
is give me out laser light
and let us say this typical laser point that
we seen i the lab you know in the auditorium
is let's say this is of power twenty mini
watt a twenty mini watt power is coming out
and since laser light is go as a beam let
us say the radios of this beam is one millimeter
therefore what you want to know is how much
pressure 
does this laser apply on a surface where it
is completely absorbed so what we are seeing
is i have a surface on which the laser beam
which is coming let's absorbed completely
the pressure comes because of the momentum
transferred per unit area percent unit time
is equal to the pressure
we have a area is equal to pi r square which
is ten raise to minus six pi metre square
we have power which is equal to twenty milli
watt or two times ten raise minus two watts
and therefore the s or the pointing vector
is going to be two times ten raise to minus
two divided ten raise to minus six pi which
is two times ten raise to four over pi joules
per second meter square that is s s is equal
to u time c where u is the energy density
and therefore u is equal to s over c which
is equal to two times ten raise to four over
pi times three times ten raise to eight which
is two over three pi times ten raise to minus
six joules per metre cube
how much the momentum carry momentum for that
is momentum across a surface percent unit
area per unit time is u which is two over
three pi times ten raise to minus six now
i can write it as moment so k g meter per
second per unit area percent unit time and
this is the moment on transfer and this is
therefore going to the pressure which comes
out to be point six seven over three roughly
point two two ot two point two times ten raise
to minus seven newton's per metres square
that's the answer
so what i have shown you to through this examples
is that how much is roughly filled associated
with radiation that we seen our last slides
and also how much is the pressure you see
that field are quietly large of the order
of ten volt per metre and pressure applied
by light is very very small of the order of
ten raise to minus six or ten raise to minus
seven newton's per metres square
