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4.6 Fields in a Cyclotron
Watch: Physics in Action: Electromagnetism and Circular motion in a Cyclotron
http://www.triumf.ca/home/for-media/publicationsgallery/videos/e-m-and-circular-motion
1) Linear Accelerator: 4:30 – 5:50
a) Why are electrostatic forces used to accelerate the ions and not gravity or magnetic forces?
Gravity is too weak and magnetic forces act perpendicular to velocity and so can’t speed up.
b) Why does TRIUMF accelerate hydrogen ions instead of hydrogen atoms?
Electric forces only act on charged particles.
c) TRIUMF uses 300 000 V for the initial kick. How fast do the protons go?
½ mv2 = qV
v = sqrt(2qV/m) = 7.58 x 106 m/s
2) Quadrupole Focusing: 5:50 – 6:45
The charges in beam repel each other and the beam tends to spread out. The diagram below shows a
cross-section of the beam with five negative ions. Draw a force diagram of the four electric forces acting
on the shaded particle
3) Electrostatic Beam Steering: 6:45 – 7:40
a) Make a large labelled sketch of the curved charged plates used to turn the hydrogen ions. The radius
of curvature is 0.32 m and the separation between the plates is 0.038 m. Include the field lines and
the charges on the plates. Draw the ion in two places and show the direction of the force on it.
b) The acceleration is 1.52 x 10 1014 m/s2. Why is it so huge? What is the potential difference on the
plates to provide this acceleration?
a = v2/r
The speed is huge and squared and the radius is small
a = F/m = q  /m = qV/md
V = a m d/q = 6.0 x 104 V
4) The Cyclotron: 7:40 – 9:08
a) Make a sketch of the cyclotron and its electric and magnetic fields.
b) What are the jobs of each field?
The electric field speeds up the particles and the magnetic field turns them.
c) Why must the electric field change direction every half period?
The force must switch directions because the velocity does.
d) How does the ion speed depend on radius?
A) v varies as r
B) v varies as 1/r
C) v does not vary with r
qvB = m v2 /r
v = q B r/m (A)
e) How does the cyclotron period depend on radius?
A) T varies as r
B) T varies as 1/r
C) T does not vary with r
qvB = m 2 v/T so
T = m 2qB 
It travels farther and faster, same time. (C)
f) Graph the following speed (vertical) vs. radius and find the slope.
r (m)
3.81
4.50
5.59
8
v(m/s)x 10
1.10
1.37
1.63
7.80
2.25
7.92
2.30
g) What physical quantities determine the slope? qvB = m v2 /r
v = (qB/m) r
h) Why is electromagnetic steering chosen for high speeds instead of electrostatic?
A stronger force is needed for a larger speed and the magnetic force increases with speed.
i) What field is needed for a velocity of 1.00 x108 m/s and a radius of 2.6 m?
B = vm/qr = 0.40 T
9) The steering magnet: 9:08 – 9:50
a) The steering magnet has an iron core and an air gap. Why?
The iron core strengthens the field and the gap provides space for the particles to pass through.
b) Sketch the electromagnet showing field lines, current, iron and the air gap.
c) The strength of the field in the air gap is given by B = NI/h, where h is the size of the air gap. The
magnet has 84 turns, an air gap of 0.10 m and can handle up to 540 A. What is the field strength?
B = (6100) 4 10-7 (84) (540)/0.10 = 3.5 x 103 T
Note : 6 100 is the permeability forn iron given p. 390 of the textbook/
Textbook: 8.2
p. 427 # 8 – 12, 428 # 16 – 19