Current Density Video Lecture | Physics for JAMB

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going ahead with this one now we'll talk
about current density you remember when
we talked about current being a scalar
or a vector I told you that current is a
scalar quantity but there is another
quantity which is a vector quantity and
which takes care of the direction part
involved in a current so now let us talk
about current density it is basically a
property which describes at a specific
point of the conductor so that means
like let us suppose if I have a
conductor if I say what is the amount of
current that is flowing through this
particular point of the conductor at
that time current density plays a role
so current density is nothing but the
current flowing per unit area provided
the area is held normal to the current
so in this case current density is
current flowing per unit area but this
area here is not a scalar quantity this
area is an area vector here we have also
spoken about area vector when we when we
were studying about flux right in one of
our previous lessons so area vector is
something where the not only the
magnitude of the area but also the
orientation of the area plays an
important role so current flowing per
unit area vector is current density so
as the orientation of the area changes
the amount of current flowing through
the area also changes right so current
density is generally denoted by a
capital J so we can write it as J is
equal to I per unit area it is a vector
quantity that is the most important
point here now let us understand the
area vector part in this way let us
suppose you have this
Adie where this arrow comes and strike
right now let us suppose if the board is
located in this way if the board is
situated in this orientation what
happens when all the arrows come they
come and directly strike the board so if
you see there were a total of six arrows
here seven arrows and all of them were
able to strike the wood now if I change
the orientation of the board in this way
it is slightly oriented making some
angle theta with the y-axis now in this
case what happens not all but only three
of the arrows could touch the board now
let us suppose if I change the
orientation all the more and make it
flat of the ground in this gate what
would happen we see that not a single
arrow is able to touch the wood that
means the amount of current which is
flowing even though the current which
started initially remains the same but
depending on the orientation of the
board the amount of current which
actually flown which actually had flown
changed right so this shows that the
current flowing that is the current
density changes as the orientation of
the area changes so this is this is why
area is looked at as a vector quantity
in this case because the orientation of
the area plays a very important role
here so we call it as area vector and
that is why we consider current density
as a vector quantity so when we define
current density there also very clearly
mention that it is the current flowing
per unit area provided the area is held
normal to the current that means the
current is flowing in this direction the
area has to be held like this so only in
that case current density would mean the
current flowing per unit area because
otherwise the current flowing would not
be the correct current flowing right
because if your area is changing its
orientation the amount of current flow
is also changing so here let me make it
mathematical so that it becomes easy for
you as I told the
current density can be written as the
change of current with unit area so this
can be written like this where area
means area vector right so J dot Da is
equal to D I now what is this this is
nothing but this is nothing but J into
da cos theta which is equal to the
amount of current which is flowing
through this area da now when this area
vector is perpendicular to J that means
let us suppose this area vector is
perpendicular to J in that case theta
will be equal to 90 degree therefore cos
theta is equal to 1 therefore J da will
be equal to D I so we say that in this
case I will be equal to J a or we can
say J is equal to I per unit area so J
is equal to AI per unit area is true
only when the area vector is held normal
to the direction of the current thank
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