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Coulomb's Law

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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 …show more content…

Calculations To determine if Fc is inversely proportional to r2, we calculated Fc and 1/r2. Several other calculations were made before we were able to arrive at these values. In table 1, columns 1 and 2 are data. Columns 3 and 4 are the coordinates of the ball and prod in meters. The conversion was made using the following equation. xm = (xp - 109.2)/.1112 where xm is the coordinate in meters, and xp is the coordinate in pixels. This equation was found by graphing pixels vs. meters for known values along a meter stick. The graph was linear with an R 2 value of 1.000, and the equation of the least squares fit line was used to convert from pixels to meters. The distance between the prod and the ball, r, is the difference in the two coordinates; r = xp - xb where xp is the x coordinate of the prod and xb is the x coordinate of the ball. Column 7, 1/r2 was computed from r. The distance from equilibrium, x, was calculated using x = xe – xb where xe is the coordinate of equilibrium. The magnitude of the repulsive force, F c, is found using the equation derived earlier, adding the mass of the string to the mass of the ball. Results: If Fc is inversely proportional to r2, then a graph of Fc vs. r should yield an inverse square relationship. A data summary is shown in Table 1 below.

Table 1: Summary of Coulomb Data

As shown in Figure 4, when the video analysis is done carefully and modeled with Fc = Const./r 2 ,

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