5Motion of a charged particle in the magnetic field
5Motion of a charged particle in the magnetic field.docx
Teacher Guides of the Lesson
Theoretical material for the lesson,
definitions for concepts
A bubble chamber
image of the tracks of subatomic
tracks curve because the charged
affected by the presence of a magnetic field.
Moving Moving particles
The world of
atomic physics is populated by a greatvariety
of particles – electrons, protons, neutrons, positrons and many more. Many of
these particles areelectrically charged, and so
their motion is influencedby electric and
magnetic fields. Indeed, we use thisfact
to help us to distinguish one particle from another.Figure shows the tracks of particles in a detectorcalled a bubble chamber. A photon (no track) hasentered from the top and collided with a proton; theresulting spray of nine particles shows up as the gentlycurving tracks moving downwards. The tracks curvebecause the particles are charged and are moving ina magnetic field. The tightly wound spiral tracks areproduced by electrons which, because their mass issmall, are more dramatically affected by the field.In this chapter, we will look at how chargedparticles behave in electric and magnetic fields andhow this knowledge can be used to control beams ofcharged particles. At the end of the chapter, we willlook at how this knowledge was used to discover theelectron and to measure its charge and mass.
An electron beam tube (Figure 2) can be used to demonstrate the
magnetic force on a moving charge. A beam of electrons is produced by an
‘electron gun’, and magnets or electromagnets are used to apply a magnetic
You can use such an
arrangement to observe the effect of changing the strength and direction of the
magnetic field, and the effect of reversing the field. If you are able to
observe a beam of electrons like this, you should find that the force on the
electrons moving through the magnetic field can be predicted using Fleming’s
left-hand rule. In Figure 3, a beam
of electrons is moving from right to left, into a region where a
magnetic field is directed into the plane of the paper. Since electrons are
negatively charged, they represent a conventional current from left to right.
Fleming’s left hand rule predicts that, as the electrons enter the field, the
force on them will be upwards and so the beam will be deflected up the page. As
the direction of the beam changes, so does the direction of the force. The
force due to the magnetic field is always at 90° to the velocity of the
electrons. It is this force that gives rise to the motor effect. The electrons
in a wire experience a force when they flow across a magnetic field, and they
transfer the force to the wire itself. In the past, most oscilloscopes,
monitors and television sets made use of beams of electrons. The beams were
moved about using magnetic and electric fields, and the result was a rapidly
changing image on the screen.
The magnetic force on a
We can make an intelligent
guess about the factors that determine the size of the force on a moving charge
in a uniform magnetic field (Figure 4). It will depend on:
■■ the magnetic flux density B (strength of the magnetic
■■ the charge Q on the particle
■■ the speed v of the particle.
The magnetic force F on
a moving particle at right angles to a magnetic field is given by the equation:
F = BQv
The direction of the force can
be determined from Fleming’s left-hand rule. The force F is always at
90° to the velocity of the particle. Consequently, the path described by the
particle will be an arc of a circle.
If the charged particle is
moving at an angle θto the
magnetic field, the component of its velocity at right angles to B is v sin
θ. Hence the equation becomes:
F = BQv sin θ
We can show that the two
equations F = BIL and F = BQv are consistent with
one another, as follows.
Since current I is the
rate of flow of charge, we can write: I = Qt
Substituting in F = BIL
gives: F = BQL
Now, Lt is the speed νof the moving particle, so we can write:
F = BQv
For an electron, with a charge
of −e, the magnitude of the
force on it is:
F = Bev (e = 1.6010−19
The force on a moving charge
is sometimes called ‘the Bev force’; it is this force acting on all the
electrons in a wirewhich gives rise to ‘the BIL force’.Here
is an important reminder: The force F is alwaysat right angles
to the particle’s velocity v, and its directioncan be found
using the left-hand rule (Figure 5).
Instructions for demonstrations and
Warning: experiments with electricity should be performed under the
supervision of teachers or adults familiar with electricity safety procedures.
Additional guidelines for organizing a
moment. Establishing emotional state. Checking for absent students.
shows a picture on presentation and asks students: Why the electron beam is deflected as
it passes through charged metal plates?
3.Individual students were called on to
respond to questions and share their own opinions/thoughts. Then she explains
that the tracks curve because the charged
particles are affected by the presence of a magnetic
introduces the topic and objectives of the lesson, assess criteria.
5.If a fine
beam electron tube is not available, teacher
just uses a picture of electron beam tube and describes the effects of magnetic fields on moving charges
6.Teacher leads learners to derivation of the formula F = BQv
sin θ. Use
the Fleming’s Left Hand Rule to find the direction of Lorentz
asks learners to take cards (one side is empty, another side has a name of a
group) and to divide into two/three groups. They answer questions step by step
Teacher check and assess students ability to use Fleming’s left hand rule to determine the velocity of a charge, the direction of the
magnetic field, and the direction of the magnetic force on a moving charge.
Assessment criteria and score for each round should be agreed in advance.
the end of the lesson students are encouraged to reflect on what they have
they need to improve.
Recommendations for formative assessment
Activity 1. Students
discuss learning objectives and assess criteria.
Activity 2. Individual
students were called on to respond to the teacher question related to the
picture and share
their own opinions/thoughts.
Activity 3. Learners
derive the formula by Teacher's Support F= BQv sin θ. Use the Fleming’s
Left Hand Rule to find the
direction of Lorentz
take cards (one side is empty, another side has a name of a group) and
two/three groups. They answer questions step by step in groups. They are
and assessed by a teacher for ability to use Fleming’s left
hand rule to
the velocity of a charge, the direction of the magnetic field, and the
of the magnetic force on a moving charge.
Activity 5. At the
end of the lesson students are encouraged to reflect on what they have learned
what they need to improve.
Answers, criteria for
assignments, additional materials for the lesson
ØI Round – Multiple choice Question 
ØII Round – Test Yourself 
ØIII Round – Problem solving 
Multiple choice question (2
A charged particle is situated
in a region of space and it experiences a force only when it is in motion.
Which of the following states the field or fields enclosed in the region
A) An electric field only
B) Both a magnetic field and
an electric field
C) Both an electric field and
a gravitational field
D) Both a magnetic field and a
E) A magnetic field only
Explanation: Magnetic fields exert forces on charged particles only if those
particles are moving.
Test Yourself (2 score)
to the following information for the next two questions.
If the orange diamond particle
shown above is negatively charged, in which direction is the magnetic force
acting on it while it is at the position shown?
the right side of the page (+x)
the left side of the page (-x)
the top of the page (+y)
the bottom of the page (-y)
of the above
False? As the magnetic
force acts on the particles shown in the diagram above, it does work on each
one. This would be evidenced by a change in the kinetic energy of each particle.
3. What is the direction of
the magnetic field that produces the magnetic force on a positive charge as
shown in each of the three cases in the figure below, assuming is
perpendicular to ?
(c) Out of
Solving problem (3 score)
4. A cosmic ray proton moving
toward the Earth at 5.0 ∙ 107 m/s experiences a
magnetic force of 1.70 ∙ 10-16 N. What is the strength
of the magnetic field if there is a 450 angle between it
and the proton’s velocity?
•B = F / qv 
•B = 1.70 ∙ 10-16 N / 1.6
∙ 10-19 C × 5.0 ∙ 107 m/s 
•B = 3.0 ∙ 10-5 T
List of useful links and literature
Douglas C. Giancoli, Physics Principles with
Applications, Seventh edition 2014.
David Sang, Graham Jones, Gurinder Chadha and Richard
Woodside, Cambridge International
AS and A Level Physics CoursebookSecond Edition, 2014