PASCO ES-9070 COULOMB BALANCE - Manual (Page 12)

Coulomb Balance 012-03760E
8
➁ Plot q versus R 2
Either of these methods will demonstrate that, for relatively large values of R, the force is propor-
tional to 1/R 2 . For small values of R, however, this relationship does not hold.
Corrections to the data
The reason for the deviation from the inverse square relationship at short distances is that the charged
spheres are not simply point charges. A charged conductive sphere, if it is isolated from other
electrostatic influences, acts as a point charge. The charges distribute themselves evenly on the
surface of the sphere, so that the center of the charge distribution is just at the center of the sphere.
However, when two charged spheres are separated by a distance that is not large compared to the size
of the spheres, the charges will redistribute themselves on the spheres so as to minimize the electro-
static energy. The force between the spheres will therefore be less than it would be if the charged
spheres were actual point charges.
A correction factor B, can be used to correct for his deviation. Simply multiply each value of q by 1/
B, where
B = 1 – 4
a 3
R 3
;
where a equals the radius of the spheres and R is the separation between spheres.
To correct your data:
➀ Calculate the correction factor B for each of the separations R that you used. Record your results in
Table 1.
➁ Multiply each of your collected values of q by 1/B and record your results as q
corrected
.
➂ Reconstruct your graphs relating force and separation, but this time use q
corrected
instead of q. Make
your new plot on the same graph as your original plot. How does the correction factor affect your
results?
(Part B) Force Versus Charge
With the sphere separation (R) held at a constant value (choose a value between 7 and 10 cm), charge
the spheres to different values and measure the resulting force. Keep the charge on one sphere
constant, and vary the charge on the other. Then graph angle versus charge to determine the relation-
ship.
The charge can be varied using either of two methods:
Method I:
If your power supply is adjustable, simply charge the spheres to different potentials, such as 7, 6, 5,
4, and 3 kV. (When charging the spheres, they should always be at their maximum separation.) The
charge on the sphere is proportional to the charging potential.
Method II:
If your power supply voltage is not adjustable, the charge can be changed by touching one or both of
the spheres with an identical sphere that is discharged. The charge will be shared equally between the
charged and discharged sphere. Therefore, touch the charged sphere once to reduce the charge by
half, twice to reduce the charge by 1/4, etc.