let us study about the deflection of a moving
charge by a sector of magnetic field. in this
figure you can see, between 2 parallel boundaries,
in a region of width d. a magnetic field sector
is created. and the value of magnetic induction
is given as b. now if a charge particle with
a charge plus q moving with a velocity vector
v. enters into, the sector of magnetic field
in the direction normal to it. we know by,
righthand palm rule the magnetic force will
act on it in upward direction that you can
calculate either by flemings rule or righthand
palm rule. the magnetic force will act on
it in upward direction. and along this line
only there exist, a centre of circular path
along which it’ll move. and with respect
to this centre when the charge particle will
move. and in this situation the radius of
this circle can also be given as m-v over
q-b which we already studied. and when it
reaches the other boundary it’ll be ejected
out tangentially later on it’ll continue
to move in the straight line. and from the
original direction of motion. you can see
the direction is deflected by some angle.
and here you can see this is the angle of
deviation delta by which the charge particle
is deviated. so, we can say by using this
sector. we can deviate the charge particle
to any extend depending on the magnitude of
b as well as the width of this sector. and
this delta we can easily calculate. like in
this situation if this angle is delta. this
will be. pie by 2 minus delta. and hence this
will also be delta because this angle is 90
degree so this will be the deviation angle
delta. as the sector width is d. here we can
write. in this triangle. sine delta we can
write as d by r. so here angle of deviation.
of charge particle by the sector can be given
as sine inverse of, d by r. if you substitute
the value of r over here delta we can write
as sine inverse of. q-b-d over m v that is
total deviation. suffer by the charge particle
in its motion when it passes through the,
sector of this magnetic field of width d.
provided here the value of sector width. should
be less then. the radius of charge particle,
here you can see if this d is more then the
radius of charge particle it’ll not reach
the other boundary. it’ll complete the semicircle
and come out like in this situation. if another
charge q moves with velocity v. such that
v is small. and, in the line of, magnetic
force if the radius is small because it depends
on the momentum of particle and if speed is
less. the radius will be less. it’ll complete
the semicircle. as, we can say here it is
not be able to reach the other boundary it’ll
come back. in the same direction so here deviation
angle will be equal to 1 80 degree or pie
radians. this is the way how. we analyze the
motion of charge particle in the magnetic
field.
