Download Lab 4: Magnetic Force on Electrons

Lab 4: Magnetic Force on Electrons
Introduction:
Forces on particles are not limited to gravity and electricity. Magnetic forces also exist. This magnetic force is known as the
Lorentz force and it is proportional to the charge, its velocity, and the magnetic field strength. In one respect the magnetic force
is truly unique - its direction. It is perpendicular to the velocity of the particle and field and so does no work – not now or ever.
The sum of all electric and magnetic forces on a charged particle is written as: F = qE + qv×B . (Note: the cross product gives
the orthogonal character to the magnetic force whose direction is indicated by the right-hand rule.) In this lab, the full electric
and magnetic field interaction with an electron is studied. By the end of this lab you should:
• Confirm the existence of the magnetic force
• Solve for the trajectory of an electron in electric and magnetic fields
• Understand how and where magnetic force applies to the real world
Materials:
• Cathode ray tube (CRT)
CRT
• 0-1000 VDC (0.3 mA) power supply to create electric fields
• Wire coil (S)
• 0-10 VDC (1 Amp) power supply to create magnetic field
• Voltage, Current, and Gauss meters
• Caliper or ruler for measuring CRT beam displacement
Barry C. Walker
Department of Physics and Astronomy
[email protected] 302- 831- 2673
S
1
Copyright University of Delaware, 2005. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.
Experiment 1 –The apparatus for this experiment consists of an
D1
electron tube, called a cathode ray tube – CRT - since the electrons
D2
coming from a negative “cathode” were originally thought to be
rays. The electron “gun” in the CRT produces a beam of electrons
F
on the face of the CRT. The CRT is a vacuum environment so the
H
electrons do not collide with gas atoms in the tube. The figure shows
the electron gun inside of a CRT.
Plug in the cathode ray tube and the accelerating voltage, adjust the
focus to achieve the sharpest spot, and mark the point at which the
interact with electrons. The electron gun in the CRT has deflection
plates (see figure). Using your controls to to adjust the voltage on the
Insulator
Band
goal of this first experiment is to first determine how electric fields
High
Voltage
Acceleration
Region
electron beam is displayed with a grease pencil on the screen. The
Figure: Side and end on view
of electron gun. The electrons
“boil off” the heated cathode
(H) and are accelerated and
focused to a beam by the
focusing grids (F). Horizontal
(D1-left/right) and vertical
(D2-up/down) deflection plates
direct the electron beam.
Low
Voltage
Gun
Region
which form a spot of fluorescent light where they excite the atoms
plates and the distance the electrons move on the screen via F=qE,
which you should understand quite well by now. Describe how you
believe the potentials and fields in the deflection plates work.
Also, sketch the trajectory of a deflected electron in the CRT.
Over most of the CRT the electron energy is given by the high
voltage region of 250V. When the electron has 250V of energy,
calculate its velocity in the CRT.
Barry C. Walker
Department of Physics and Astronomy
[email protected] 302- 831- 2673
2
Figure: A cut away view of a CRT. The gun produces the beam of
electrons. These are then accelerated after the insulator to a high
voltage where they strike the screen and excite the phosphor. These
excited atoms quickly radiate this energy in the form of light.
Copyright University of Delaware, 2005. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.
Experiment 2 - The goal of this experiment is to determine how magnetic
fields interact with electrons. With the electron deflection set to zero and the
magnetic field OFF, i.e. the beam in the center of the screen, there is no
transverse electric or magnetic force on the electrons in the CRT: F = qE +
qv×B = 0. The electrons are traveling straight to the screen with the velocity
from experiment 1.
Now, turn on the power supply to the wire coil to generate a magnetic field. A
few amps of current should be enough to create the magnetic field. The force is
not zero from the magnetic field and you should observe, as Lorentz observed,
Figure: The CRT setup with the magnetic field
from the coil of wire. The vertical component of
the magnetic field is being measured.
there is a magnetic force F = qv×B.
To quantify this interaction, use your gauss meter to measure the magnetic
field from the wire coil. A picture of the B field lines from a wire coil is shown
in the figure. Note the field changes direction (line direction) and magnitude
(represented by the field line density) for various positions from the coil. You
will need the “vertical” component and magnitude of the field in the central
region where the electron traverses to calculate the changes in the electron
trajectory. Since the field is fairly uniform, take the average reading for the
vertical component of the B field around the CRT (see figure). Measuring a
vector field is tricky so spend 15 minutes or so to make sure you are measuring
Figure: Magnetic Field from a loop of wire or
circular dipole magnet. Note, the magnetic field is
a vector! You need to quantify the component
interacting with the electron.
the field magnitude and direction correctly.
Barry C. Walker
Department of Physics and Astronomy
[email protected] 302- 831- 2673
3
Copyright University of Delaware, 2005. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.
Now, you will need to quantify the force on the electron as a function
magnetic shielding
L
of the B field. Measure the deflection, “x,” of the electron beam on the
screen for three different magnetic fields. Construct a plot of x versus B
electron gun
on a graph for four or five different magnetic fields. An electron moving
at constant velocity through a uniform magnetic field perpendicular to
the velocity is deflected from a straight line to a circular path. Since the
electron has a constant velocity and magnetic field is reasonably
uniform, the electron will move in a circular arc (see you text for
electron motion in uniform magnetic field).] You may remember the
acceleration experienced by an object in a circular path of radius R is |a|
= v2/R where ma = Fcir. Based on the deflection, x, you have measured
R
φ
Figure: Circular
arc deflection of electron
beam for constant V and B.
Note: B=0 inside the shielding.
and the geometry of the CRT (i.e. the length L), determine the radius of
curvature R for the curved path of the electron beam. Finally, use this
radius and the mass of the electron to determine the Force on the
electron.
Now, using a second method check the Lorentz Force formula. With
the electron velocity, electron charge, magnetic field, calculate the
Lorentz Force, Fmag = qv x B. Compare this to the Force you measure
Figure: With the cover of a TV set removed, the CRT is easy to
identify. You can also see the high voltage cable that provides the
final acceleration voltage. (picture from www.howstuffworks.com)
in the experiment and see if these forces equate.
Barry C. Walker
Department of Physics and Astronomy
[email protected] 302- 831- 2673
4
Copyright University of Delaware, 2005. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.
Experiment 2: Real World Problem:
A television set or computer monitor is a cathode ray tube. Here is the
problem – MULTIMEDIA! Everyone wants a huge 22” high-resolution
monitor and a hi-fidelity sound system with 8” subwoofer. Unfortunately,
magnetic fields from the speakers really mess with the electron on their
way to the phosphor screen. This interaction is the same reason you get a
“rainbow of color” when you put the refrigerator magnet next to your TV
when you were little. You can assume the magnetic field from the speaker
magnet is 50 Gauss at a distance of 0.2 meter from the center of the
speaker. Also note that one pixel of deflection will destroy the image.
• For a typical monitor, what magnetic field strengths can be tolerated in
Figure: Traditional color CRT monitors used for
computers offer an impressive 1000 or more pixels in
screen sizes up to 22” for less than $1000.
the vicinity without distorting the image?
• How much would the magnetic field from an 8” subwoofer need to be
reduced to eliminate distortion? I.E. how much shielding / attenuation
should the engineers consider?
Figure: The full experience in multimedia now involves
vision and sound. Perhaps tactile senses in the future?
Barry C. Walker
Department of Physics and Astronomy
[email protected] 302- 831- 2673
5
Copyright University of Delaware, 2005. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.