Coulomb's Law
Purpose The purpose of this experiment is to test Coulomb's Law which states that the force between two spherically symmetric charged objects is directly proportional to the product of the charges, and inversely proportional to the square of the distance between the centers of the two charges. In mathematical vector notation Coulomb’s Law is expressed as
where Fr is the force on particle 1 due to particle 2 in Newtons, q is the charge on 12 1 particle 1 in Coulombs, q2 is the charge on particle 2 in Coulombs, rˆ12 is a unit vector originating at the center of particle 1 and pointing directly away from particle 2, r is the distance between the centers of the two particles in meters, and k is a constant, given by
Introduction Coulomb formulated his law and tested it using a device he called the torsion balance. One sphere suspeded from a fiber has the same charge as a second sphere. These spheres are charged in the same manner so they repel each other. This causes the the fiber supporting one of the spheres to twist. To measure this repulsive force, Coulomb counter-acted the repulsive force by twisting the suspension head through the angle theta needed to keep the two spheres a certain distance apart. The force of repulsion was balanced by the force resulting from the twisting of the suspension head. Thus, the angle theta provided a relative measure of the force of repulsion between the two spheres. Coulomb performed a similar experiment to test the force of attraction between two spheres of opposite charges. We used the video analysis of a different set up to investigate this law. Our setup consisted of a charged ball suspended by two strings, and a charged ball mounted on a lucite prod. This is shown in Fig. 1. The prod has the same charge as the suspended sphere. Since like charges repel, the ball moves away from the prod as it is brought closer. The distance that the suspended ball moves can be used as a measure of the force of repulsion. Equations To
where Fr is the force on particle 1 due to particle 2 in Newtons, q is the charge on 12 1 particle 1 in Coulombs, q2 is the charge on particle 2 in Coulombs, rˆ12 is a unit vector originating at the center of particle 1 and pointing directly away from particle 2, r is the distance between the centers of the two particles in meters, and k is a constant, given by
Introduction Coulomb formulated his law and tested it using a device he called the torsion balance. One sphere suspeded from a fiber has the same charge as a second sphere. These spheres are charged in the same manner so they repel each other. This causes the the fiber supporting one of the spheres to twist. To measure this repulsive force, Coulomb counter-acted the repulsive force by twisting the suspension head through the angle theta needed to keep the two spheres a certain distance apart. The force of repulsion was balanced by the force resulting from the twisting of the suspension head. Thus, the angle theta provided a relative measure of the force of repulsion between the two spheres. Coulomb performed a similar experiment to test the force of attraction between two spheres of opposite charges. We used the video analysis of a different set up to investigate this law. Our setup consisted of a charged ball suspended by two strings, and a charged ball mounted on a lucite prod. This is shown in Fig. 1. The prod has the same charge as the suspended sphere. Since like charges repel, the ball moves away from the prod as it is brought closer. The distance that the suspended ball moves can be used as a measure of the force of repulsion. Equations To