let us discuss about the force between 2 parallel
current carrying wires.
here this figure shows a very long straight
wire which carries a current i-1. and at a
distance r from it another parallel wire is
placed, which is a-b of length l and it is
carrying a current i-2.
now if we wish to find out the force experienced
by the wire a-b. here if it is due to the
magnetic induction of current i-1 then we
can say due to this current i-1 magnetic induction
at wire a-b is in, inward direction.
and here we can write.
magnetic induction.
due to i-1. at the location.
of wire a-b is.
this is the magnetic induction due to, current
i-1 which can be given by the result of a
straight wire at a distance r, which can be
written as.
mu not i-1 by 2 pie r this we have already
studied by using biosavart law in previous
topic. and here if this is the magnetic induction.
by using righthand palm rule we can find out
the force experience by the wire a-b. in this
situation here we can see the realistic righthand.
which is pointing its finger in, inward direction
and thumb along the direction of current i-2,
so here you can see the force experience by
wire a-b will be towards left.
so in this situation.
we can now draw.
the force acting on wire a-b is towards left
and on wire i-1 is toward right according
to newton’s third law.
because every action has equal and opposite
reaction.
so now in this situation.
you can once again verify by your own righthand
that whether i have drawn the directions correct
or not.
here we can see this righthand again.
in realistic situation by which we can show.
that force acting on wire a-b will be toward
left.
so here we can write.
force, or rather we can write magnetic force.
on wire a-b is.
this force we can write as b-1 i-2 l which
we already studied.
which is given by b-i-l. so we substitute
the values this mu-not i-1 i-2 l, divided
by 2 pie r. this is the expression for magnetic
force between the 2 wires.
separated by distance r and 1 wire should
be very long other should be of length l.
so always remember that when 2 wires carrying
a current.
parallel wires carrying current in same direction.
they always attract each other.
similarly if the current in wire a-b is reversed
you can see.
the force on wire a-b will, start acting toward
right so on this wire.
carrying a current i-1 will also be experiencing
a force toward left.
so here we can say we can write down.
important note, that.
2 parallel wires.
carrying current.
in same direction.
always attract each other.
and carrying current.
in opposite direction.
always ripple each other.
This is quite a useful note, you should always
keep in mind, in next section we’ll study.
about some realistic situations and experiments
which are based on the magnetic force between
2 wires.
