Lecture 16
Physics II
Chapter 32
Magnetic Force
Cyclotron motion
Course website:
http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII
Lecture Capture:
http://echo360.uml.edu/danylov201415/physics2spring.html
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Department of Physics and Applied Physics
Electric Field
Magnetic Field
From Coulomb’s law
1
̂
4
Biot-Savart law
̂
4
Gauss’s Law
Ampere’s Law
∙
∙
So, now we know how to find magnetic fields using Bio-Savart and Ampere’s laws.
Now, the question is
“how does a magnetic field interact with material
(which consists of charges and current)?”
Magnetic force on
a moving charge
PHYS1440 Lecture 16 Danylov
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Magnetic force on
current
Magnetic force on
a moving charge
PHYS1440 Lecture 16 Danylov
Department of Physics and Applied Physics
The Magnetic Force on a Moving Charge
After Oersted’s discovery, there were many other experiments with magnetic fields,
currents, charges, etc. It was found that B exerts a force on a moving charge.
The magnetic force on a charge q as it moves through a magnetic field B with
velocity v is:
where  is the angle between v and B.
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The Magnetic Force on a Moving Charge
A magnetic field has no effect on a charge
moving parallel/antiparallel to the field
PHYS1440 Lecture 16 Danylov
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ConcepTest
B field of q
A) To the right

The direction of the magnetic force
on the proton is
B) To the left C) Into the screen
D) Out of the screen
E) The magnetic force is zero
ConcepTest
B field of q
A) Upward

The direction of the magnetic force
on the proton is
B) Downward
C) Into the screen
D) Out of the screen
E) The magnetic force is zero
Applications
PHYS1440 Lecture 16 Danylov
Department of Physics and Applied Physics
Magnetic Force in
“Art”
Electrons in a kinescope are deflected by a magnetic field
Nam June Paik’s Magnet TV (1965) at the truly amazing new Whitney Museum of American Art.
My face (without a magnet)
Nam June Paik
(a Korean‐American artist)
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Magnet TV
1965/99 There is an amazingly beautiful application of Cyclotron Motion
Many important applications of magnetism involve the motion of
charged particles in a perpendicular magnetic field
PHYS1440 Lecture 16 Danylov
Department of Physics and Applied Physics
Cyclotron motion
The figure shows a positive charge moving in a plane that is
perpendicular to a uniform magnetic field.
B into page
Since F is always perpendicular to v,
F changes the direction of the velocity, but not
it is magnitude.
It means q experiences only the centripetal
acceleration
Thus, the charge undergoes uniform circular
motion.
This motion is called the cyclotron motion of
a charged particle in a magnetic field.
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Cyclotron radius
Newton’s second law for a radial direction,
B
The radius of the cyclotron orbit:
If B=0, then rcyc=0, which is a straight line
The period of the cyclotron motion:
The frequency of the cyclotron motion.
Note! The cyclotron frequency does not depend on v.
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Department of Physics and Applied Physics
Cyclotron motion
 The figure shows a more general situation in
which the charged particle’s velocity is not
exactly perpendicular to B.
∥
B
 The component of v parallel to B
is not affected by the field, so the charged
particle spirals around the magnetic field lines
in a helical trajectory.
 The radius of the helix is determined by v,
the component of v perpendicular to B.
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Aurora (Northern lights)
Charged particles
(solar wind)
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The Cyclotron
The first practical particle
accelerator, invented in the
1930s, was the cyclotron.
Cyclotrons remain important
for many applications of
nuclear physics, such as the
creation of radioisotopes for
medicine.
PHYS1440 Lecture 16 Danylov
Department of Physics and Applied Physics
ConcepTest Mass Spectrometer
x x x x x x x x x x x x
Two particles of the same mass
enter a magnetic field with the
same speed and follow the paths
shown. Which particle has the
bigger charge?
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x x x x x x x x x
A
B
C) both charges are equal
D) impossible to tell from the picture
,
, , The relevant equation for us is:
.
According to this equation, the
bigger the charge, the smaller the radius.
Follow-up: What is the sign of the charges in the picture?
If q > 0, then the force is to the left (our case)
Cloud/Bubble chamber to detect
charged particles
(contains a supersaturated vapor of water)
The photograph shows the track of an
unusual positively charged particle with a
mass about equal that of an electron slowed
down by passing through a lead plate. It
lead plate was among the earliest evidence of the
existence of the positron found by C.D.
Anderson in 1932, but predicted by Paul
Dirac in 1928
A gamma photon kicks out an electron out of an atom and creates an electron‐positron pair.
PHYS1440 Lecture 16 Danylov
Department of Physics and Applied Physics
Magnetic force on
Current-Carrying
Wires
PHYS1440 Lecture 16 Danylov
Department of Physics and Applied Physics
Magnetic Forces on Current-Carrying Wires
We saw that a magnetic field exerts a force on a charge. A current consists of
many moving charges, so a magnetic field should exert a force on a current.
The magnetic force of a charge:
The magnetic force on a segment dl:
If we apply this formula for a straight wire with a current I, then we will get:
Where l is a part of wire exposed to the magnetic field
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Magnetic Forces on Current-Carrying Wires
∥
There’s no force on a currentcarrying wire parallel to a
magnetic field.
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End of class
Magnetic Forces on Current-Carrying Wires
 A current perpendicular to the field
experiences a force in the direction of
the right-hand rule.
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Magnetic Forces Between Parallel CurrentCarrying Wires: Current in Same Direction
Let’s find a force on current I1
We’ll treat I2 as a source of the magnetic field
Demo: Forces on a Current‐Carrying Wire
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Magnetic Forces Between Parallel CurrentCarrying Wires: Current in Opposite Directions
PHYS1440 Lecture 16 Danylov
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Slide 32-147
Summary
Electric Field
Magnetic Field
From Coulomb’s law
1
̂
4
Bio-Savart law
̂
4
Gauss’s Law
∙
∙
Amperian loop
The electric force on a charge:
The magnetic force on a charge:
The magnetic force on a current:
PHYS1440 Lecture 16 Danylov
Department of Physics and Applied Physics
What you should read
Chapter 32 (Knight)
Sections
 32.7 (Skip the Hall effect)
 32.8
 32.5 (skip)
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Thank you
See you on Friday
PHYS1440 Lecture 16 Danylov
Department of Physics and Applied Physics