Sierzega: Magnetism 4
Magnetic Force Exerted by a Magnetic Field on a Single Moving Charged Particle
If a magnetic field exerts a force on current carrying wires, is it reasonable to believe that the magnetic
field also exerts a force on individual moving electrically charged particles (electrons)?
4.1 Observe and find a
pattern A cathode-ray tube
(CRT) is part of a
traditional television set or
of an oscilloscope.
Electrons “evaporate” from
a hot filament called the
cathode. They accelerate
Hollow
anode
Hot
cathode
–
–
+
–
Scintillating
screen
electrons
across a potential difference and then move at high speed toward a
scintillating screen. The electrons form a bright spot on the screen at the
point at which they hit it. A magnet held near the CRT sometimes causes the
electron beam to deflect.
a. Watch the video at
http://paer.rutgers.edu/pt3/experiment.php?topicid=10&exptid=114
or use the QR code at the right.
b. Devise a rule for the direction of the force Fm that the magnet exerts on the moving electrons
relative to the direction of their velocity v and the direction of the magnetic field B produced
by the magnet. Use the information provided in the table. (The red side of the magnet is the
north pole.)



Experiment
Observation
Point the north pole of a magnet at the front of the
Nothing happens to the beam.
scintillating screen—opposite the direction the electrons are
moving.
Point the north pole of the magnet from the right side (as
you face the coming beam) perpendicular to the direction the
electrons are moving.
Point the south pole of the magnet from the right side
perpendicular to the direction the electrons are moving.
Point the north pole of the magnet from the left side (as you
face the coming beam) perpendicular to the direction the
electrons are moving.
Point the south pole of the magnet from the left side
perpendicular to the direction the electrons are moving.
Point the north pole of the magnet down from the top of the
CRT, perpendicular to the direction the electrons are
moving.
Point the south pole of the magnet down from the top of the
CRT, perpendicular to the direction the electrons are
moving.
Sierzega: Magnetism 4
c. Your friend says that the beam of electrons is deflected by the magnet because the electrons
are charged particles and the magnet is made of iron. Because all conductors attract
electrically charged particles, the experiment above is not related to magnetism. How can you
convince your friend that she is mistaken?
4.2 Represent and reason For each situation below, decide if a non-zero magnetic force is exerted on
the moving electric charge (test object). If not zero, indicate the direction of the magnetic force.
(a)
(b)
(c)
(d)
(e)
into paper
(f)
=0
(g)
(h)
into paper
out of paper
4.3 Derive Using the equation for the magnitude of force that a magnetic field exerts on a current
carrying wire, develop an expression for the magnitude of the force that the magnetic field exerts on
a single charged object with charge q moving at speed v. To help, begin by thinking of the current I
in the wire as a large number of positively charged particles, each with a charge q, that pass a cross
section of wire in a time interval Δt.
Sierzega: Magnetism 4
Magnetic force exerted by magnetic field on a charged particle
The magnitude of the magnetic force that a magnetic field exerts on a particle with electric charge q
moving at speed v is:
FB on q = |q|vBsinθ
Where θ is the angle between the direction of the velocity of the particle and the direction of the B-field.
The direction of this force is determined by the right hand rule for the magnetic force. If the particle is
negatively charged, then the force points in the opposite the direction.
What is the magnitude of force if the velocity and the B field vectors are parallel?
When is the magnitude of the force maximum?
4.4 Particles in a magnetic field Each of the lettered dots shown in Figure below represents a small
object with electric charge of +2.0 x 10-6 C moving at the speed of 3.0 x 107 m/s in the directions
shown. Determine the magnetic force (magnitude and direction) that a 0.10-T B-field exerts on each
object. The B-field points in the positive y direction. Hint: First, use the right hand rule for the
magnetic force to determine the directions of the magnetic force exerted on each object.
Sierzega: Magnetism 4
4.5 Represent and reason The mass-detecting part of a mass spectrometer is described below in
multiple ways.
Words
Sketch
Physical
Mathematical
representation
representation
An ion with mass m and
Top view
charge +e leaves a velocity
selector moving at speed v.
∑Fradial = m ac
. .
.
It then moves in a half
Velocity
circle in a magnetic field
Fm = m v2/ r
selector
. .
.
that is perpendicular to the
radial
+
2r
plane of its motion. At the
e v B = m v2/ r
. .
.
end of this trip, it is
detected. The radius of the
or
Detector
circle can be used to
. .
.
determine the mass of the
m = eBr/v
ion.
.
Are the representations consistent with each other? Notice that this problem involves a charged particle
moving in an external magnetic field whose origin is unknown.
4.6 Motion of protons in Earth’s magnetic field What happens to a cosmic ray proton flying into
Earth’s atmosphere above the equator at a speed of about 107 m/s? The average magnitude of Earth’s
B-field in this region is approximately 5 x 10-5 T. The mass m of a proton is 1.67 x 10-27 kg. Consider
(i) a proton moving perpendicular to the B-field lines and (ii) a proton moving at an angle θ relative
to the B-field lines.
4.7 If the magnetic force is always perpendicular to the velocity of a charged particle, does it do any
work on it? Explain your answer.