PASCO ES-9070, Instruction Manual And Experiment Manual, Page: 13 / 22

012-03760E Coulomb Balance
9
(Part C) The Coulomb Constant
In parts A and B of this lab, you determined (if all went well) that the electrostatic force between two point
charges is inversely proportional to the square of the distance between the charges and directly proportional
to the charge on each sphere. This relationship is stated mathematically in Coulomb’s Law:
F = k
q
1
q
2
R
2
;
where F is the electrostatic force, q
1
and q
2
are the charges, and R is the distance between the charges. In
order to complete the equation, you need to determine the value of the Coulomb constant, k. To accom-
plish this, you must measure three additional variables: the torsion constant of the torsion wire (K
tor
), so you
can convert your torsion angles into measurements of force, and the charges, q
1
and q
2
. Then, knowing F,
q
1
, q
2
, and R, you can plug these values into the
Coulomb equation to determine k.
Measuring the Torsion constant, K
➀
Carefully turn the Torsion Balance on its side,
supporting it with the lateral support bar, as shown
in Figure 7. Place the support tube under the
sphere, as shown.
➁
Zero the torsion balance by rotating the torsion
dial until the index lines are aligned. Record the
angle of the degree plate in Table 2.
➂
Carefully place the 20 mg mass on the center line
of the conductive sphere.
➃
Turn the degree knob as required to bring the
index lines back into alignment. Read the torsion
angle on the degree scale. Record the angle in
Table 2.
➄
Repeat steps 3 and 4, using the two 20 mg masses and the 50 mg mass to apply each of the masses shown
in the table. Each time record the mass and the torsion angle.
➅
Complete the table as follows to determine the torsion constant for the wire:
a. Calculate the weight for each set of masses that you used.
b. Divide the weight by the torsion angle to determine the torsion constant at each weight.
c. Average your measured torsion constants to determine the torsion constant for the wire. Use the
variance in your measured values as an indication of the accuracy of your measurement.
ä NOTE: A torsion constant for a wire usually expresses the torque required to twist the wire a unit
angle, and is normally expressed in newton meters per degree. However, when using the torsion balance,
the torque arm is always the same (the distance from the center of the conductive sphere to the torsion
wire), so the torsion constant for the balance is more conveniently expressed in newtons per degree.
copper rings
support
tube
lateral support bar
Figure 7. Calibrating the Torsion Balance
center
line
mass