in this example, we are given that the figure
shows a horizontal wire m-n. which is of length
l and mass m is placed in a magnetic field
b. and we also given that the ends of the
wire are bent and dipped in 2 bowls containing
mercury. which is connected to an external
circuit we can see here a battery and resistance
are there. and if the key is pressed for a
short time delta t. due to which a charge
q flows. we are required to find the maximum
height above initial level the wire m-n will
jump. now in this situation for solution we
can see. when the switch is pressed. for a
time delta t a current flows. and due to this
current we can see by righthand palm rule
we can say that the wire will experience a
force in upward direction which is b-i-l.
and, as this force is applied for a time delta
t it’ll experience an impulse in upward
direction. which will impart in initial velocity
v to the wire. so here we can write. by impulse.
of magnetic force. we can write the impulse
will be b-i-l delta t which will be imparting,
a momentum to the wire m-n so we can write
its initial speed is v. so the momentum imparted
will be m-v. and in this situation i delta
t is the amount of charge which is passed
through the wires for which we already given
that the total charge q flows. so here this
will give us the value of initial speed imparted
to the wire that is b. i delta t we can write
as q it’ll be. b q l divided by m. that
is the initial velocity imparted to the wire.
now in the situation if this is the initial
speed. as soon as it’ll jerk off the contact
with the. mercury in the balls will break,
and it will decelerate with the gravity that
is the deceleration g. so in this situation
the maximum height attained by the wire can
be simply given by the speed equation. so
the initial speed is v we can write maximum
height attained. by wire m-n. is. maximum
height we can directly write as v square by
2 g. so on substituting the value of this
speed we are getting the result as. b square
q square, l square by 2 m square g, that will
be the answer to this problem.
