Download Motion of Charged Particles in Magnetic Fields File

Le Fevre High School
SACE Stage 2 Physics
Motion of Charged Particles in Magnetic Fields
1.
A proton moves vertically down at 6.7 x 107 m s-1 through a north-south
magnetic field of 7.3 x 10-3 T. Calculate the magnitude and direction of the force
that acts on the proton.
2.
A positively charged carbon ion (mass 2.00 x 10-26 kg and charge 1.60 x 10-19 C)
moves in a circular path of radius 0.20 m. A magnetic field of 0.50 T is
perpendicular to the plane of the circular path. Calculate the speed of the
carbon ion.
3.
A certain charge moving north at 3.00 x 102 m s-1 enters a region in which there
is a 5.00 x 10-6 T field acting vertically downward. The charge undergoes
circular motion in a clockwise direction with a centripetal force of 3.00 x 10-3 N
acting. Find the nature and size of the charge.
4. A proton is accelerated from rest through a potential difference of 1.7 x 105 V and
enters a magnetic field having a strength of 0.20 T. Determine the:
(a) speed of the proton,
(b) radius of the path of the proton,
(c) time for one revolution of the proton.
5.
An electron moving at 7.00 x 105 m s-1 enters a region in which a uniform
magnetic field exists and describes a circle of radius of 0.640 m. Find:
(a) the magnetic field strength in this region,
(b) the period of revolution of the electron.
6.
As seen in the diagram over the page, a beam of particles of charge q enters a
region where an electric field is uniform and directed downward. Its value is 80
kV m-1.
(a) Write down an expression for the magnitude of the force ‘F’ acting on the
charge due to the electric field in terms of ‘q’ and the electric field strength
given.
Perpendicular to E and directed into the page is a magnetic field B = 0.4 T.
(b) Write down an expression for the magnetic force acting on the charge in terms
of ‘q’, the speed ‘v’ and the magnetic field strength given.
If the speed of the particles is properly chosen, the force due to the electric field
and that due to the magnetic field will be equal in magnitude. What speed is
selected in this case? (This device is called a velocity selector.)
Le Fevre High School
E = 80 kV m-1
FB
+q
v=?
B = 0.4 T (into
the plane of the
page)
FE
7.
A beam of cathode rays (electrons) is found to move in an arc of radius 0.45 m
in a magnetic field of strength 300 T. Calculate the speed of the cathode rays.
8.
The A cyclotron has a radius r and a magnetic field of strength B. It is used to
accelerate particles of mass m, carrying a charge q.
(a)
Show that the period T of the motion of the particles in their circular
2m
paths is given by T 
.
qB
(b)
Show that the kinetic energy K of the emerging particles is given by
q2 B2r 2
K
2m
9.
the
be
from
The Dees of a cyclotron have a diameter of 90cm. The magnetic field inside
evacuated Dees is 1.9T. This cyclotron is used to accelerate protons.
(a)
Find the period of the motion of the protons.
(b)
What is the frequency of the alternating potential difference that must
applied to the Dees?
(c)
Determine the energy (in electron volts) of the protons that emerge
this cyclotron.
(d)
Consider a cyclotron that is identical to the one above except that its
diameter is twice as great. What effect would this have on,
(i)
the period of the protons.
(ii)
the kinetic energy of the protons.