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)
• 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
CRT
Experiment 1 –The apparatus for this experiment consists of an
electron tube, called a cathode ray tube – CRT - since the electrons coming from a negative “cathode” were originally thought to be rays. The electron “gun” in the CRT produces a beam of electrons which form a spot of fluorescent light where they excite the atoms on the face of the CRT. The CRT is a vacuum environment so the 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 electron beam is displayed with a grease pencil on the screen. The goal of this first experiment is to first determine how electric fields interact with electrons. The electron gun in the CRT has deflection plates (see figure). Using your controls to to adjust the voltage on the 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.
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.
D1
D2
F
H
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.
High Voltage Acc
el e ration Region In su lator Ban d
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, 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 the field magnitude and direction correctly.
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.
Figure: The CRT setup with the magnetic field from the coil of wire. The vertical component of the magnetic field is being measured.
Now, you will need to quantify the force on the electron as a function 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 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 = F
cir. Based on the deflection, x, you have measured
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
in the experiment and see if these forces equate.
Figure: Circular arc deflection of electron beam for constant V and B. Note: B=0 inside the shielding.
L
φ
R
magnetic shielding electron gun
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)
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 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: Traditional color CRT monitors used for computers offer an impressive 1000 or more pixels in screen sizes up to 22” for less than $1000.
Figure: The full experience in multimedia now involves vision and sound. Perhaps tactile senses in the future?
