012-03760E
Coulomb Balance
15
Teacher’s Guide
Experiments: Parts A-C
Torsion Wire Calibration
J
J
J
J
J
J
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0
100
200
300
400
500
600
700
Force (N)
Angle (degrees)
f(x) = 1.448574E-6*x + 4.496489E-6
R^2 = 9.998832E-1
➤
NOTE: The slope of this curve is dependent
on the tension on the wire; thus, it will be slightly
different for each unit.
Distance Dependence
5
5
5
5
5
5
5
5
5
5
5
5
5
0
50
100
150
200
250
300
350
400
0
2
4
6
8
10
12
14
16
Angle
Distance (cm)
f(x) = 3.3 * (x^-1.0 )
R^2 = 9.959050E-1
A power regression of this data shows that there is
an inverse-square dependence, as predicted by
theory.
Charge Dependence
ä NOTE: There are two ways of verifying the
dependence of force on charge. You may hold
one of the spheres at a constant charge and show
that force is linear with the other charge, or you
may charge both spheres equally and show that
the force is proportional to the square of the
charge. The latter method is easier to control with
a single voltage supply, and was used for this
write-up.
J
J
J
J
J
J
J
J
J
0
20
40
60
80
100
120
0
1000
2000
3000
4000
5000
6000
Angle (degrees)
Potential (V)
f(x) = 1.335407E-5 * (x^1.0 )
R^2 = 9.954969E-1
y= 3.071653E-6*x^2+4.0;
R^2 = 9.967336E-1
The first equation given here (a power regression)
shows that the force is dependent on the square of
the charges, as predicted by the equations.
The second curve fit (a programmed least-squares
fit), when converted to SI units, gives us a value of
1.05x10
10
for k. This value is 17% higher than the
accepted value of 9 x 10
9
. We do not know the
reason for this error at the time this is being written.
If you have any explanations for this error, or
suggestions about how to improve it, please let us
know. Call PASCO Technical support at (800) 772-
8700.
