in this example we are given that a rod a-b
of mass m is placed on 2 smooth rails p and
q. in a uniform magnetic induction b as, we
can see in figure. and it is saying that the
rails are connected to a constant current
source of current i. and we are required to
find the speed attain by the rod a-b when
it leaves of the other end of the rails. now
in this situation lets have a look on the
situation when. the source provides a current
i. this current i will be flowing through
the wire, in downward direction. and the magnetic
induction b. here we can see by righthand
palm rule the wire will experience the magnetic
force toward right and that will be equal
to b-i-l. due to which the wire will accelerate
and if the wire is starting from one end of
the wire when it’ll reach the other end.
it would have covered total distance l that
is equal to the length of the rails. so when
it’ll break off it’ll move off, with the
speed v from these rails. so here we can write.
acceleration of rod. a-b. when. it slides.
on rails. is. this acceleration we can write
as b-i-l upon m because it’ll experience
a constant force because there is a constant
current source over here. now after traveling
a distance l. we can write final speed. attained
by rod. this can directly be given as v square
is equal to u square plus 2 a-l and as initially
the rod was starting from rest. from the initial
stage. so u can be written as zero. so here
the speed we are getting is root 2 a-l on
substituting the values the speed we are getting
is root of. 2, b, i l, l by m. that will be
the answer to this problem.
