Coulomb's Law


To verify the proportionality of Coulomb's Law that the electric force between two point charges is directly proportional to the product of the charges and is indirectly proportional to the square of the distance between them.


Coulomb's Law gives us the static electrical force F, exerted by a point charge Q1 on another point charge Q2 in terms of r, the distance between them :

F = Q1 Q2 / (4 pi eo r^2)

In this experiment, we will verify this law and enroute learn how to use an optical lever to magnify a small rotation into a large displacement. Finally we will learn about systematic errors and how to correct for them.

PreLab Homework

The prelab homework must be done at home and handed to the lab TA before you start the lab.

Questions :

The Experiment


The verification of Coulomb's Law proceeds as follows :


The actual experiment will be executed as follows :

I. Setting it up

II. Measuring the relaxation time of the torsion fiber

Although we are interested in the static deflection theta of the optical lever system to infer the force F, we have to acknowledge that this system is a torsion oscillator and the transient behavior to static changes must be determined. There is an oscillatory period t0 and a damping or relaxation time tr. The angular displacement due to these transients is given by :

theta( t ) = theta0 exp ( - t / tr ) cos ( 2 pi t / t0 )

from where we can see that at time t = t r

theta( t ) = theta0 exp ( -1 ) ~ theta0/3

(Here we have used the fact that for critical damping, t0 ~ tr ). So the reason we wait till the displacement becomes a third of the original theta0 is that the time interval t then equals tr. tr is called the " relaxation time" and is the approximate time that the torsion oscillator takes to settle down to its equilibrium value. Actually 1/3 is here an approximation for the number 1/e = 1/ 2.71... and is therefore not fundamental and is only an approximation.

Each time we vary the charge or the distance, we should wait ~ 3tr seconds before taking down a reading.

III. Measuring the leakage of charge

Because of air currents and humidity, charge tends to leak off from the spheres. The leakage is not negligible and has to be accounted for. This will enable you to make a correction to the charge in your later measurements.

IV. Varying the charge Q1

Now we will actually begin making measurements to test Coulomb's Law. In this section we vary the charge Q1.

V. Varying the distance r between the spheres

The procedure is similar to that of Part IV above.

VI. Leakage of charge ( again )

Due to possible changes in humidity and other conditions of the air we measure the decay curve and plot it on the same graph as Part III above.

Data Analysis

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