Principle of superposition - Electric Charges & Fields Video Lecture - Class 12

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before going ahead with part 11 so now
we will talk about something called
principle of superposition
what will principle of superposition
tell us it will basically talk about the
scenarios where we have multiple charges
in the system till now I defined
Coulomb's law
considering that there are two charges
right so the force on one charge due to
another charge but now let us suppose
that they retain charges in the system
so what will be the net force on one
charge the net force on one charge will
be because of the other nine charges
right so principle of superposition
tells us about the scenario where we
have to calculate the net electrostatic
force on one charge due to multiple
charges present in the system so the
principle of superposition states that
the total force on a given charge due to
a number of charges is the vector sum of
the individual forces exerted on that
charge by the other charges that means
let us suppose that if I have one charge
if I have a charged one two three four
five so charge on one is equal to the
vector sum of the forces due to each of
these charges that means force on one
due to two plus force on 1 to 2 3 plus
force on 1 due to 4 plus force on one
give to 5 so it is the vector sum of the
forces on that particular charge due to
all the other charges each individual
force is unaffected by the presence of
the other charges that means force on
one due to two is independent of how
many other charges are present there
right so let us suppose in there are 20
charges present so the force exerted on
a particular charge due to some other
charge is not dependent on the other
charges other 18 charges which are
placed
they're right at me so let us look at it
in the vector form let us suppose that
we have a particular charge say q1 since
we are considering a system with
multiple charges so let us suppose these
are the other charges say Q 2 Q 3 Q 4
and so on similarly you have many other
charges and let us say this is any
generalize child cqm so you have
multiple charges in a system and let us
denote their position vectors as R 1 R 2
R 3 R 4 so on and this's our n right so
these are the position vectors for each
of these charges so let us calculate let
us calculate the total force on Q 1 so
let us suppose that we want to calculate
the total force on Q 1 so according to
the principle of superposition the total
force on Q 1 will be equal to the force
on Q 1 due to Q 2 plus force on Q 1 due
to Q 3 and so on that means the total
force on 1 that is F 1 total will be
equal to force on 1 due to 2 plus force
on 1 DV 3 plus force on 1 due to 4 and
so on till force on 1 due to the NX
charge like this is what the principle
of superposition States so now let us
calculate each of these values so let us
calculate F 1 2 that is force on 1 due
to 2 so before this we will apply
Coulomb's law which says K Q 1 Q 2
divided by r 2 1 square R 1 unit vector
similarly let us calculate F 1 3 so this
will be equal to K Q 1 Q 3 divided by R
3 1 square into R 3 1 unit vector
similarly we can write F
one n will be equal to K Q 1 Q n / r n 1
square into R and 1 unit vector now
putting all these values you can find
out the expression of F 1 so what will
be the expression for F 1 so your F 1
will be equal to K you can take common
so inside you will have Q 1 Q 2 divided
by r 2 1 square into R 2 1 unit vector
plus Q 1 into Q 3 divided by R 3 1
square into R 3 one unit vector plus so
on
you go to the NH term which is Q 1 Q n
divided by r n 1 square into r N 1 unit
vector so this is what you get so
therefore you can write F 1 is equal to
F 1 2 plus F 1 3 plus so on till F 1 n
similarly you can calculate similarly
you can calculate the total force on Q 2
so that will be equal to force on 2 to
do 2 1 + force on 2d root 3 plus dot dot
dot he'll force on to do 2 in its charge
and similarly you can write it for F 3 F
4 and so on therefore in general we can
say that force on any eyuth charge that
is denoted by I that is for any charge Q
1 Q 2 Q 3 Q 4 or whatever is equal to K
into summation of Q I Q n divided by ad
n I into unit vector R
five n-i right so what is I here I is
nothing but values from 1 to N so if you
see this we have just written the same
expression which we wrote here this
expression only we have written it in
general form so this is nothing but the
expression the concise expression for
the principle of superposition so this
expression defines the principle of
superposition right I think it is clear
to you now principle of superposition
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