q/m FOR THE ELECTRON
Name: ____________________
Class:_____________________
Pre-Lab Questions Page
Roster#____________________
Instructor:__________________
1. List the magnitude of an electron’s charge and mass in standard SI units.
q = _________________
m = ________________
2. Calculate the magnitude of the ratio of an electron’ charge to its mass,
according to the values listed in the textbook. Use SI units.
3. When an electron travels through a constant magnetic field, the electron’s
velocity ________ and the speed ___________.
a.
b.
c.
d.
changes, changes
remains the same, changes
changes, remains the same
all the above
4. A proton is moving along the y-axis in the positive y-direction and
experiences a magnetic force that is in the negative x-direction. (a) What is the
direction of the magnetic field the proton is traveling through? (b) Redo this
question but this time use an electron.
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q/m FOR THE ELECTRON
OBJECTIVE:
To measure the ratio of the charge to mass for an electron.
APPARATUS:
q/m Apparatus including High Voltage Power Supply
Magnetic Field Power Supply
Meter Stick
Digital Ammeter
INTRODUCTION:
A stream of electrons is accelerated through a measured potential
difference and then passes perpendicularly through a uniform, variable magnetic
field provided by a pair of Helmholtz coils. The magnetic force, FB, on the beam
of electrons causes them
to deflect in a circular
Ammeter
path. The force acting on
Variac
1234
the charge, q, moving
Coil
with a velocity, v, High
perpendicular
to
the Voltage
magnetic field B, is given
by:
FB = qvB
Equation 1
Vm
6.3 V
Newton's second
law for an electron of
mass m, moving in a
circle of radius r, may be
expressed as:
Coil
Figure 1
mv 2
= qvB
FB = mac =
r
Equation 2
The electron gains its final velocity by accelerating it from rest through a
large potential difference ∆V. From the work-energy principle
1 2
mv = q∆V
2
Equation 3
Combining equations 2 and 3 and solving for ∆V yields:
2 2
⎛ q ⎞⎛ B r ⎞
⎟⎟
∆V = ⎜ ⎟⎜⎜
⎝ m ⎠⎝ 2 ⎠
1
Equation 4
The magnetic field is provided by a pair of Helmholtz coils, which
produce a uniform magnetic field over a large area between the coils.
The magnitude of this magnetic field is given by:
⎛
1 ⎞
⎟
B = 8µ oNIm⎜
⎝ 125 R ⎠
Equation 6
The symbol µo = 4π x 10-7 Tm/A and is known as the permeability of free space,
and N = number of turns that the coil has, Im = current through the magnet and R
= radius of the Helmhotz coil.
PROCEDURE:
NOTE: BE VERY CAREFUL--HIGH VOLTAGES ARE BEING USED!
There is a danger of electrocution.
1.
Be sure the circuit is connected as shown in figure 1 and that all switches
are in the OFF position. The high voltage adjust should be all the way
forward. DO NOT adjust the variable ac for this entire experiment.
2.
Turn on the high voltage power supply. The switch is on the back of the
unit. Wait 2 minutes for the high voltage power supply to stabilize, then
adjust to 2.00 kV. A blue trace should be visible across the tube. (If no
trace appears get the lab instructor.)
3.
Turn on the power supply for the magnetic field coils (∆Vm) and the
ammeter. Adjust the voltage knob on this power supply until the ydeflection is y = 2.4 cm at x = 10 cm. Record this current.
4.
Repeat steps 2 and 3 for High Voltages of 3.00 kV, 3.50 kV, 4.00 kV and
4.50 kV. Turn the High Voltage down to 2.00 kV.
5.
Turn the voltage of the magnetic field power supply (∆Vm) to its lowest
setting. Turn it off and reverse the leads on this power supply. Turn this
power supply back on and adjust the voltage knob until the deflection (in
the opposite direction) is again y = 2.4 cm at x = 10 cm.
6.
Repeat step 5 for High Voltages of 3.00 kV, 3.50 kV, 4.00 kV and 4.50
kV.
7.
Turn down the magnetic field power supply (∆Vm) to its lowest value and
turn it off. Turn the High Voltage to zero and turn off this power supply.
8.
Record the radius, R, of the Helmholtz coils to the uncertainty implied and
also the number of turns. This should be on the back of the equipment.
CALCULATIONS:
1.
Using the values of x = 10 cm and y = 2.4 cm, compute the radius of the
path of the electron beam from the equation:
2
x2 + y2
2y
For each value for the High Voltage applied to the plate of the q/m tube
you should have two values for the current in the magnetic field coils.
Average the absolute values of these currents for each High Voltage.
r=
2.
3.
B2r 2
for each High Voltage then produce a graph of High
2
B2r 2
Voltage versus
. (Use Graphical Analysis),
2
Compute
4.
Use the slope of this graph and Equation 4 to determine the experimental
value of q/m for an electron.
5.
Calculate the %Error between your experimental value and the theoretical
value of q/m for electrons.
QUESTIONS:
1. An electron in a television picture tube moves toward the front of the tube
with a speed of 8.0 x 106 m/s along the x-axis. Surrounding the neck of
the tube are coils of wire that create a magnetic field of magnitude of
0.025 T, directed at an angle of 60o to the x-axis and lying in the xy plane.
Calculate the magnetic force on and acceleration of the electron. Hint:
Think Newton’s 2nd law when solving for the acceleration.
2. Rework question #1 using a proton instead of an electron.
3. An electron beam is projected to the right. The beam deflects downward
in the presence of a magnetic field produced by a pair of current-carrying
coils. (a) What is the direction of the magnetic field? (b) What would
happen to the beam if the current in the coils were reversed?
4. Calculate the speed of the electron using the experimental data, the graph
and equations 2, 3 and 4.
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