Relation between Electric Field & potential - Electrostatic Potential & Capacitance Video Lecture - Class 12

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16 now let us find out a relationship
between electric field and electric
potential so let me use the notation so
that it becomes easier for you to
understand electric field E and electric
potential V so we will find out a
relationship between these two so for
that let us consider equipotential
surfaces let us suppose we have these
two equipotential surfaces one surface
is at some potential V let us suppose
one of the surfaces is at potential V
and the other surface is at potential V
Plus Delta V let us suppose the
potential at this surface is V it is of
course potential at the surface is V and
this surface is V Plus Delta V now and
we have a small charge say DQ we want to
take this small charge DQ from a point
on a surface to another point on the
other surface let us suppose we want to
take this charge from point A to point B
now we so we have what do we have we
have a small charge DQ which we move
from A to B so whatever works there for
some amount of work is also done by
removing this charge so what is that
small amount of work then we know that
work done is equal to what it is equal
to the small is equal to the charged
particle deficit that is Q into the
potential difference between a and B so
what is the potential difference VB will
cancel so Delta V is the potential
difference right so
is the small amount of work done to take
this particle from one point to another
but also we know that work done can also
be written as dot product of force and
displacement so this can be written as f
into d ad into cos theta so what is
Theta theta will again be 180 degree
that's because the force and the
displacement they are always in the
opposite direction in this case because
the electric force acts along the
direction of electric field and the
direction of electric field is this this
is the direction of electric field and
the particle is taken from A to B right
so these two directions are totally
opposite so this is cos 180 which
becomes equal to F minus F into di now
what does this F this force arises due
to electric field so we can write it as
minus e into d cube into d ad now if you
look at this equation and this equation
what do you see the left-hand side of
both the equations are same therefore
from 1 & 2 we can say that DQ into Delta
V is equal to minus e DQ into di so DQ
DQ will get cancelled therefore we say
that e is equal to minus D V by D and
that means electric field is equal to
the change of this the change of
electric potential with distance right
so this is the relationship between
electric field and electric potential so
what does this thing regarding the
direction of electric field it says that
the electric field is always along the
direction where the potential decreases
steepest that means where the putting
decrease in potential is good the
electric field is always along that
direction so it is along Direction where
potential
big creases thirsty best that means the
decrees of potential is maximum so
electric field will be along that
direction and what it does it tell about
the magnitude it tells that potential
per unit displacement perpendicular to
the equipotential surface so when we
talk about the magnitude of electric
field it is potential per unit
displacement perpendicular to
equipotential surface at that point
right so please remember this
relationship because this is going to
help you a lot when solving your
numerical problems now that we have
reached towards the end of discussion on
electric potential let us have quick
round of discussion on electric
potential energy as well I mean I have
already discussed about it thank you
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