Cartesian Coordinate Systems, EMFT, Electrical Engineering, GATE Video Lecture

now let's move on to the differential
elements in the Cartesian coordinate
system so here we know that this XYZ is
the condition for the system and the
differential element we have to convert
it in F del X del Y or don't a
differential element system means we are
taking a very small quantity it is
called a and with the point P we are
just changing the direction or the
location of the point P which is making
a small Q which is going to be like this
let us take this is the red X if this is
the direction you see the by X or the CP
x axis and we are making assuming there
is small Q which is going to be like
this see this morning to be resuming and
if I consider a point P which is get the
location of this vertex is at the point
P and if I'm moving from this point to
this point that means we are giving a
small displacement of X by a chain
making a point P dash so we can assume
that p is having the coordinates of X
file and J and the pedestrian obtaining
from the small displacement that is for
a Dell then in coordinate of X plus 10 X
it should be my plus del Y and if you do
J plus Delta so that means this is more
the displacement in Del Y which is
called as more displacement and one this
is just a small displacement will are
polling at Avenger and similarly that we
are calling it del X del X in the
direction of X del J in the direction of
Z and del Y in the connection off but if
I point to find it if you want to find
the distance between P and P dash vector
then how we can go like this person we
can do this let us take this is the
small point O and here the Boca distance
here do you get distance if I just
write the equation for the copy desk for
me consider that we are already done it
should be X the X cap plus my divisor
plus Jack which should be gave get there
and the distance from copy - weapon
should be equals to X plus 10 X 15 X cap
plus y plus del Y D my 10 plus 10 plus
10 that should be a jet and if you want
to define the disturbed on P - P - then
it can be calculated like this person BP
- should because - whoopee - vector
minus mu P vector so we can buy it you
should me give you - vector for vehicles
to focus nothing but the difference
between the test two vectors that we are
obtaining is powered with 4x t display
XK plus sigma dan but if I get should
you then get a vector this is the
differential length that we are
obtaining here in the system which is
called the in the Cartesian system we
are aiming to differential elements like
this so in the differential elements
basically we have to build with the
differential nine it is for differential
nine is identical to get with the
differential surface and thought them we
are into the differential mode this top
term differential basically useful in
order to find the intensity order
quickly law and any force on each charge
that we are discussing in the to detect
a number two what is the significance of
this part why we are doing this
basically we are just assuming this
small displacement from the any sphere
or any child line on any any kind of the
under term and just by making anything
goes from differential length you can
see potential transfer function that we
can say
like this to say dimension man which is
nothing but del X Y X depth plus driver
you might have eternity
so this little keep in mind what we are
is no medical in just now in different
medicals okay must we can move to body
to function one loop when I'm sorry one
would be we should be custom red X if
identify this is the follow-up on the
differential okay now let's move on to
the the third important part that we are
going to discuss which is very very
important which is very very important
because if we understand this concern
that we can easily solve all the new
medical care will discuss in the coming
classes so it is called differential one
which is very very funny ring transfer
case general formula to represent any
differential circles turn the home to
the formula is very simple it is like
this and the s surface vector vector is
having a magnitude first show me the
magnitude like this and it's having the
unit vector which is normal to the
surface but this is basically nothing
but a unit vector or we can say like
this is the unit vector or consider the
area vector so firstly we have to
understand what is the significance of
the in ableton irrigate is a vector
which is always having a making an angle
of 90 degree with respect to the surface
but suppose if they see the surface like
expression so the area vector of the
surface is physically the magnet agree
to the surface similarly if the surface
is going to be like this the area vector
of the surface is basically of four
direction which is 90 degree it may be
worse
why or maybe of what with maybe the -
mind similarly it could be head let may
be about Jade on doing - but the area
vector is always perpendicular to the
surface
they keep this concept in the mind that
the area vector of any process of
recording if my half of any surface is
having a direction which is normal and
in the normal to the surface if I
consider the sphere or incident that
like if the cylinder is there the area
vector field ended nothing but this is V
which is normal surface because surface
is curved area vector which is making an
agreement between two surfaces variable
did nothing but V vector which is a
long-gone which is along the direction
of the increasing plus it should be
Norman who sufficient that means it get
to making an angle of 90 degree with
resin cupola so protector forgiving to
the area vector to keep in me for this
concept you're going to use in this
coordinate system so we have seen that
the cube is having mix six phases to let
or draw the pupil in
when I just draw a cube again different
will be like this
okay here we can say that this is
nothing but the J this is he considered
this is the one is injured and here
because the genitive and the idea of a
vector of J is nothing but this would be
a genitive for labor it is possibly he
might care for their certificate any a
accident we know that we for me have
done only if I want to define the area
vector of this Q then how we can proceed
we can assume there are six surfaces
this is the surface one that is called
the front surface similarly there is a
surface which is called the back surface
okay
similarly there is a surface which is
nothing but the left I divide the
surface which is the left circle
beautified surface top and the bottom
and front nd for each and individual
sorry there should be a table for this
surface which is towards the right the
area vector basically which is making an
angle of 90 degree so it should be like
this in the direction of the K by M okay
the area vector for the backside it
should be like this you fill in - divide
em if we are thinking about the top
direction the area vector is basically
it should be normal to the component to
make a 90 degree angle it should be a
jet can we talk and for you for you to
bottom we can say it should be - AJ
similarly for linear vector for the
front surface so the front surface
having a video vector off in the
direction of ax mr. da is kept and for
the back surface we can say it should be
- exp so this is the significance of the
area vector and that the help of is
confirmed we can define the differential
surface so if we're defining
the differential surface for the ds5
vector from vehicles to in the direction
of the gave a vector here the dy is
nothing but this would be this is for DX
and near the image actually this is DJ
so DX multiplied by T del X multiplied
by Delta in the direction of device it
is con the area vector for this y
component
this is galaxy for because the DX did
your good taking a Dell or D is
basically is to simply just just you are
just I am for the PDF for you to be to
be X digit and it gets basically be
microphone okay if I just want to write
the the X vector so where the X
component is bigger which is moving like
this and if you provide the equation for
the various component is a dy or digital
is similarly we can tally the the s J
vector from Greek Festival in direction
of rigid because magnitude and direction
I need to attach is in magnitude having
if this is d1 and this is this is this
is basically nothing but the area vector
direction for tip or the area vector
equations for T say our Cartesian
coordinate system so I think you will
understand the differential and event in
the Cartesian system how we can define
the equations just to making a vector
which is normal to the plane surface
making an nth degree barracuda this is
the concept regarding the Cartesian
coordinate system