Download Exploration: Moving Particles in Magnetic Fields

Exploration: Moving Particles in Magnetic Fields
In this lesson you will use the "Particle in a Magnetic Field" applet to investigate
the behaviour of charged particles moving through magnetic fields.
Prerequisites:

You should be familiar with the equation Fmagnetic  qvB which relates the
magnitude of the magnetic force on a charge 'q' moving with a velocity v at
right angles to a magnetic field of strength B.

You should know how to use the concept of inward force to explain
mv 2
circular motion and be able to use the expression Finward 
(this is also
r
often called the centripetal force).

You should know how to use the hand rules that relate the direction of the
magnetic force to the direction of motion of the charge and direction of the
magnetic field.
Learning Outcomes:
When finished, you should be able to determine the energy of a charged particle
of known mass by measuring the radius of curvature of its path as it travels
through a known magnetic field.
Making predictions
1. In the space below, draw a Free Body Diagram that shows the force that a
magnetic field directed out of the page will exert on a charged particle
moving to the right.
2. Explain why this force will cause the particle to move in a circular arc as
long as it remains inside the magnetic field. Do this by making several
drawing of how the force vector on the particle will change during small
steps of time.
mv 2
to derive an expression
r
that shows how the radius of the path of an object will be related to its
velocity, mass and charge. Write your derivation in the space below.
3. Use the equations Fmagnetic  qvB and Finward 
4. Predict how the paths of a proton, electron, muon and alpha particle will
differ if they all have the same velocity through a magnetic field of strength
1 T. (No numerical calculations required). Order these from smallest
radius path to largest radius path.
5. Predict the radius of the path taken by an alpha particle that is moving with
a speed of 60 000 km/s through a magnetic field of strength 2T.
Testing your predictions
To answer the following you should use the applet Particle in a Magnetic Field.
1. Complete the following table in which you sketch the path of an electron,
muon, proton and alpha particle. Indicate the radius in each case as well
as whether the particle is +ve or -ve in charge. Use B = 2 T and v = 60 000
km/s (Note: the applet will automatically re-scale depending on the type of
particle selected - be sure to measure and record the radius of each path
to decide how to rank them.)
Particle
electron
proton
muon
alpha
Sketch of Path
+ or – Radius
charge
(m)
Exploring the interaction between particles and magnetic fields
In this section you will use the applet to explore how the path of a charged
particle in a magnetic field is influenced by the field strength and direction as well
as the particle's mass, charge and velocity.
1. Complete the following table by filling in the missing blanks. Make sure to
choose the proton as the reference particle for this applet (from the
Options menu). Use vo = 20 000 km/s as the reference velocity.
proton
v0 = 20 000
km/s
2v0
proton
0.5v0
0.5
Out
alpha
2v0
1.5
In
proton
3v0
Particle
proton
B (T)
Direction
(In/Out)
1.5
Radius of
Path (m)
0.28 [up]
0.38 [up]
2.0
Out
0.50 [down]
2. How would radius of the path of a charged particle change if you doubled
both its mass and its speed through a magnetic field of strength B?
Explain by using the formula that you developed in section 1 above and
then confirm this by using the applet.
Determining the momentum and energy of a moving charged particle
1. It is often more convenient to express the kinetic energy of a particle using
1
p2
the equation Ek 
. Derive this equation by combining Ek  mv 2
2
2m
with p  mv .
2. Use the equations and to show that the momentum of a charged particle
moving in a magnetic field can be written as p  qBr and that the kinetic
energy can expressed as Ek
 qBr 

2m
2
.
3. Use the applet to generate a series of particle paths for which you will
measure the radius. Select the particle type from the options menu and
set a velocity and magnetic field strength by adjusting the scrollbars on the
bottom of the applet. Use the equations that you derived in #2 above to
complete the following table:
Particle
Charge
(C)
Mass (kg)
Magnetic Velocity
Field (T)
(m/s)
Radius
(m)
Momentum
(N-s)
Ek (J)