now lets discus the force on a current carrying
wire. placed in magnetic field. now say this
is the region of magnetic induction b vector
in which wire of length l. which cross sectional
area is s, and carrying a current i is placed.
now in this situation we can see that if the
current is flowing in upward direction inside
the wire free electrons would be flowing in
downward direction with the drift speed v-d.
say these are free electrons. then on each
free electron we can say it’ll experience
a magnetic force. and, total number of free
electrons in the wire can be easily calculated
by the free electron density here. say if
free electron density is given to us, at.
n electrons per meter cube. then we can write
here total number of electrons. total number
of free electrons. in wire. the wire segment
which is shown here will be equal to n-l-s.
because l-s is the volume. and small n electrons
per meter cube are the total electrons. if
we calculate the magnetic force. on each conduction
electron which is conducting electricity.
is this magnetic force on each f-m-e, can
be. calculated as. by using. laurentz force
equation it can be written as e-v-d b, because
in this situation. electronic charges e it
is moving with the, average velocity v-d and
b is the magnetic induction. and by using.
righthand palm rule we can find out the force
on this electron it is toward left here i
am keeping my fingers inward into the direction
of magnetic field. and thumb around the direction
of positive charge or current, because here
electrons are moving in downward direction.
so force on each electron will be acting toward
left. and if we calculate the total magnetic
force. on wire. or we can write total magnetic
force on all electrons it can be written as
e-v-d b. multiplied by total number of electrons
these are n-l s. and in this situation you
can see, n e v-d we can write as current density
and current density multiplied by the cross
section area we can write the total current.
as we know the value of current density is.
n-e v-d. so here current density multiplied
by the area is the current so magnetic force
on wire can be written as b i-l. this is the
expression use for. the magnetic force acting
on the current carrying wire carrying a current
i it is of length l. and the direction of
magnetic force can be. directly obtained by
using righthand palm rule. by keeping the
fingers along the direction of magnetic induction
thumb along the direction of current and palm
face will give us the direction of. magnetic
force within. total magnetic force acting
on wire will be toward left and it is given
by b-i-l. but this is the situation when wire
is placed right angle to the direction of
magnetic field. some time it happens that,
if this is uniform magnetic field. from left
to right. and in this magnetic induction we
place a wire. p-q. in which a current i is
flowing and it is of length l, so here you
can see the length of wire is placed. in such
a way that it is making an angle theta with
the direction of magnetic induction. so here
the length can be resolved in 2 components
1 will be l sine theta. and other length will
be l coz theta. here you can see this length
l coz theta is parallel to the direction of
magnetic induction. and we already studied.
a charge which flows along the direction of
magnetic induction will not experience any
force. so only the component of wire which
is perpendicular to magnetic induction will
experience. a force on it. so here we can
write. if. l vector, that is the length of
wire along the direction of current is placed.
at, theta angle. to b vector. this implies
the value of magnetic force we can write as.
b, i l sine theta we are going to use. and
in this situation the direction of magnetic
force you can see in this situation magnetic
field is toward right. and thumb i can place
in upward direction that is along l sine theta
the force will be in inward direction. so
this is the direction of magnetic force. and
this b i l sine theta can also be given in
vector form as. we can take i as scalar and.
downward direction we obtain by the cross
product of l vector and b vector so it can
be written as l cross b. this is the way how
vectorially direction as well as magnitude
of magnetic force. on a current carrying wire
placed in magnetic field can be obtained,
and if it is placed right angle to the direction
of magnetic field force will be b-i-l. and
the direction we can obtain directly by using
righthand palm rule as. what we were calculating
in case of moving charges.
