Coulomb's Law

1. Coulomb'sLaw SC442, Honors Class, Spring 2002, Dr. Roman Kezerashvili

2. Objective of the experiment: • To verify experimentally that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

3. Some theory • First of all what is an electric charge? • The electric charge is characteristic of the fundamental particles making up those objects; the world was created so that it accompanies those particles wherever they exist. • Charges of the same sign repeal to each other and charges of the opposite sing attract to each other.

4. In 1785 French scientist C.A. Coulomb did next experiment. 1 F~q1∙q2 3 F~ 4 2 F~ Where kis an electrostatic constant, k=8.98755∙109 N∙m2/c2 in vacuum.It is also visible that an electric force on each charge is directed along the line joining the charges. The electric force extends by one point charge on another along the line between the charges. The magnitude on the force is directly proportional to the product of the charges and inversely proportional to the square of the distance separating the charges. As we see the form of equation 4 looks similar to equation for gravitation force. But the difference between them is that they work with two fundamental characteristics of matter: mass and charge. Also electric interaction may be and attractive and repulsive, and gravitation interaction is always attractive. Electric force is much stronger than gravitation force. For instance we may prove that an electric force is really much stronger than gravitation force.

5. Provement that an electric force is much stronger than gravitation force through their ratio. • Let’s say there are two electrons located 1m apart. • The mass of the electron is equal to me=9.11∙10-31 kg • The charge of the electron is equal to e=1.6∙10-19C • The electrostatic constant kis 9∙109 N∙m2/kg2 • Then the electrostatic force between two electrons is equal to =2.34∙10-28 N • The gravitation constant G is 6.76∙10-11 N∙m2/kg2 • And the gravitation force between them is equal to = 5.61∙10-71 N • Then ratio of them is • As we see the electrostatic force is much stronger then gravitation force.

6. Setup for the experiment There are two identical spheres. One is mounted on a rod and suspended from a thin torsion wire. The other is mounted on a slide assembly so that it can be placed at a fixed distance from the suspended sphere. The electric force of interaction between spheres causes the torsion wire to twist through some angle θ. This angle is directly proportional to the electric force between spheres, θ~F.Therefore we shell be able to determine the force of the interaction between spheres by measuring an angle of the twist in wire.

7. To charge the spheres we use the high voltage power supply. Because the charge is directly proportional to the charging potentional q~V, we charge the spheres to different potential by touching them with a charging probe.

8. Thus, by measuring the twist angle that is portioned to the electric force and the charging potent ional, that is proportional to a charge; we establish the relationship between the electric force and the charge. This correction factor will help us correct the angle of the torsion pendulum by dividing experimental value of the angle by the correction factor.

9. Our results for the first part (the same distance & different charge) As we know, the force is proportional to the charge' product. The functional relationship between the force and the charge is a function of straight line.

11. As we said, we can consider both spheres as point charges only when the distance between them is greater than they size is. When spheres are closer, - the surface charge of the spheres is not uniform any longer. When spheres ride closer, - the correction factor B is going smaller and therefore correct angle is increasing more. This conclusion is shown clear in the graph. The sphere' radius is 1,9 cm & therefore we may consider spheres as point charges only when the distance between them is greater than 1,9cm. r a And it is also shown in this graph, - both lines follow over the same path and when we go closer to point 1.9 the separation is going bigger.

12. This is graph of the angle vs square of distance. This is graph of hyperbola because we know that angle directly proportional to inverse square of distance. But here we have square of distance (not inverse of square) and therefore we got graph of hyperbola.

13. In this picture we plotted the logarithm of the distance vs correct angle. The slope of this graph is an exponent of the variable r and it is equal to - 1.89. According to Coulomb's law this exponent should be equal to negative 2. So, our slope is almost negative 2. It is not exactly negative 2 just because there are some defects occur during this experiment. y = -1.8987x + 0.0123

14. Summary • At this experiment we found out graphically and visually validation to Coulomb’s law, we found how electrostatic force depends on distance between charged objects. Also we have seen that the force is proportional to the angle of a twist in the string of the torsion pendulum. Certainly we so that force is also proportional to the charges and inverse proportional to square of the distance between charged objects.