11 Motion of a charged particle in the magnetic field
11 Motion of a charged particle in the magnetic field.docx
Teacher Guides of the Lesson
Theoretical material for the lesson,
definitions for concepts
to find the mass of an electron first involve finding the charge-to-mass ratio e/me.
This is known as the specific charge on the electron – the word ‘specific’ here
means ‘per unit mass’. Using the equation for an electron travelling in a
circle in a magnetic field, we have e/me= v/Br.
Clearly, measurements of v, B and r are needed to measure e/me.
are difficulties in measuring B and r. For example, it is
difficult to measure r with a rule outside the tube in Figure 11.1 because of parallax error.
Also, v must be measured, and you need to know how this is done. One way
is to use the cathode–anode voltage Vca. This p.d. causes
each electron to accelerate as it moves from the cathode to the anode. If an
individual electron has charge −e then an amount of work e Vca is done on each electron.
This is its kinetic energy as it leaves the anode: eVca = mev 2
where me is electron
mass and v is the speed of the electron.
Eliminating v from the
two equations eVca = mev 2 and
r = mev/Be gives:
e/me= 2Vca / r 2B 2
Hence, if we measure Vca,
r and B, we can calculate e/me.
As we shall see shortly, the
electron charge e can be measured more directly, and this allows us to
calculate the electron mass me from the value of e/me.
Electric and magnetic fields
Now we will consider what
happens when an electron beam passes through an electric field and a magnetic
field at the same time.
Balancing the effects of
electric and magnetic fields is also used in a device called a velocity
selector. This is used in devices such as mass spectrometers where it is
desired to produce a beam of charged particles all moving with the same
velocity. The construction of a velocity selector is
shown in Figure 11.2. Two parallel plates are
situated in an evacuatedchamber.
They provide a uniform electric field of strength E.
Figure 11.2 A velocity selector – only
particles with the
correct combination of charge, mass and
velocity will emerge
through the slit S.
The region between the plates is also occupied
by a uniform magnetic field of flux density B which is at right angles
to the electric field. Charged particles (electrons or ions) enter from the
left. They all have the same charge and mass but are travelling at different
speeds. The electric force Eewill
be the same on all particles as it does
not depend on their speed; however, the magnetic force Bev will be
greater on those particles which are travelling faster. Hence, for particles
travelling at the desired speed v, the electric and magnetic forces
balance and they emerge undeflected from the slit S. If a negative ion has a
speed greater than V/Bd the downward magnetic force on it will be
greater than the
upward electric force. Thus it will be
deflected downwards and it will hit below slit S. Note that we do not have to
concern ourselves with the gravitational force mg acting on the charged
particles as this
will be much smaller than the electric and
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.
2.Teacher introduces the topic and objectives of the
lesson, assess criteria.
3.Teacher reminds learners aboutthe
bubble chamber photograph which was shown in a previous lesson and asks to share their knowledge about the importance of
finding of the speed of the particle and radius of its path, then
the specific charge/the ratio of charge to mass can be found.
learners to divide into two groups and research tasks: the charge-to-mass
ratio of an electron and velocity selection of charged particles.
suggests students to answer the Test Yourself questions. Individual
students were called on to respond to questions and share their own
asks learners to do set of calculations based on the velocity selector
can be used to assess understanding of the underlying principles and use of
end of the lesson students are encouraged to reflect on what they have learned
what they need to improve.
Recommendations for formative assessment
Activity1. Students discuss learning objectives and assess
Activity2. Students share their knowledge with a
teacher about the importance of finding of the
of the particle and radius of its
path then the specific charge.
Activity3. Learners are divided into two groups and
research tasks: the charge-to-mass ratio of an
electron and velocity
selection of charged particles. The results of group works should be
given in the form of presentations to
be defended by learners. Assessment criteria should be
agreed in advance.
the Test Yourself questions. Individual students are called on to
questions and share their own
Activity5. Learners do set of calculations based on
the velocity selector can be used to assess
understanding of the underlying
principles and use of equations.
Activity6. At the end of the lesson students are
encouraged to reflect on what they have learned
and what they need to improve.
Answers, criteria for
assignments, additional materials for the lesson
force - upwards and electric force – downwards;
∙ 103 V m−1 / 0.30 T = 5 km/s
positive ion has a speed greater than in b, the downward electric force
on it will be greater
than the downward magnetic force. Thus it will
be deflected downward and it will hit below slit S.