in this example we are given that the figure
shows a wire a-b of mass m. placed on a rough
inclined plane of inclination alpha.
it carries a current i, and we are required
to find the minimum magnitude of magnetic
induction required to slide the wire up the
inclined plane.
and here we can see the magnetic induction
is applied in the direction normal to the
plane of this inclined.
now in this situation if we draw the free
body diagram of the wire. by looking at its
cross section.
if this is the inclined plane with inclination
alpha and. in the side view cross section
say if this is wire which carries a current
i. and if magnetic induction is applied normally
to this inclined plane.
by righthand palm rule we can see that the
wire will experience a magnetic force b-i-l,
in the direction.
up the inclined. and it is experiencing its
weight mg in downward direction.
so in this situation.
in.
downward direction 1 is the component of gravity
which it’ll experience.
that will be mg sine-alpha. and.
due to the friction on the inclined plane
as it is given that it is rough inclined plane.
if we consider mu is the.
friction coefficient.
here we can write in downward direction it’ll
experience the friction as mu-n. which can
be given by. if n is the normal reaction it
can be given by the normal component of gravity
that is mg coz alpha.
so in this situation for wire.
to slide up.
the inclined.
here we can write this b-i-l must be more
then or equal to.
the downward force on the wire which have
1 component of gravity mg sine alpha plus.
the friction force limiting friction to starts
sliding that is mu n and normal reaction here
will be equal to.
mg coz alpha.
so we write it mu mg coz alpha.
so in this situation the value of magnetic
induction should be more then or equal to.
m-g. sine alpha plus mu coz alpha divided
by.
i-l. that will be the answer to question.
as this is the minimum magnitude of magnetic
induction which we require to slide the wire
up the inclined plane.
