in this example we are given that a charge
particle of mass m and charge q is accelerated
by a potential difference of v volts. with
which say it’ll attain a velocity v where
we can write q v is half m v square. and if
it enters in a region of uniform magnetic
field b as shown. we are required to find
the time after which it’ll come out from
the magnetic field. now in this situation
if we wish to find the speed we can directly
calculate as q v us equal to half m v square
because the speed is, supplied. because of
the potential difference v, by which the charge
was accelerated. now as soon as it enters
in the magnetic induction by right hand palm
rule we can find out the magnetic force acting
on it would be in this direction. and along
the line of this magnetic force there would
be somewhere the centre of circle. about which
the particle will start moving in this manner.
and it’ll complete the circle and then will
be ejected out tangentially to the circular
path, now in this situation we can see if
this angle is theta this will be 90 minus
theta and this angle will also be theta. so
the total angle for which the particle was
circulating in the circular path would be
2 pie minus 2 theta. and in this, circular
motion the angular speed of particle we know
it is given as q v by m. angular speed of
particle. during circular motion this omega
we can write as q b by m as we already studied.
that the angular speed does not depend on
the speed with which the particle is moving.
so this is angular speed total angle, it spent
in magnetic field is 2 pie minus 2 theta.
so we can directly write time spent. by particle.
in magnetic field is. this time we can simply
write as 2 pie minus 2-theta by omega. on
substituting the values the. value of time
we are getting is omega we can write as q
b by m so this will be 2 m by q-b. pie minus
theta that will be the answer to this problem.
