Two Coulomb Problems

1) Coulomb used the data from the three trials under "Experiment" in his 1785 paper (described also in Lecture 2) to derive "Coulomb's Distance Law" for repulsion of like charges:

F ∝ 1/r2

 

His data were as follows:

Wire Twist (deg)0126567
Net Deflection (deg)36188.5

How certain could he be that the exponent for r is exactly 2, and not 2 + δ ? That is

 

How large a δ could be consistent with his data?

 

(Incidentally, modern experiments, relevant to the rest mass of the photon and the dimensionality of space, show δ < 10-17)

 

Hint:  One approach would be to make a plot based on numbers derived from these data.  You might want to consider experimental error and geometry.  Detail on experiment and calculation is available in the translation of Coulomb's paper on the course website.

Click for translation of Coulomb's Paper in a new window (html) or as (PDF)

Click for Coulomb's balance diagram in a new window

 

2) Two years later (1787) Coulomb extended this law for repulsion to include attraction between opposite charges.

 

Explain why Coulomb would need to develop a different apparatus for this experiment.

 

That is, why couldn't he just use the same apparatus with different charges on the two gilded pith balls?

 

Hint: Remember that the torsional force is approximately linear in the displacement.    It might help to graph the Coulombic and torsional energies through a region including the point where they balance.