Coulomb’s Law Design Customization - Temple University Physi
Coulomb’s Law Design Customization TEMPLE UNIVERSITY PHYSICS 1 6/23/2020 1:33 PM
Coulomb’s Law explains how the electrostatic force between two point charges varies with their magnitudes and the distance separating them. The law states that the magnitude of this force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them, mathematically expressed as \( F = k \frac{|q_1 q_2|}{r^2} \), where \(k\) is the Coulomb constant (8.99 x 10^9 N·m²/C²). The force acts along the line connecting the charges, with like charges repelling and opposite charges attracting. This experiment aims to verify Coulomb’s law through measurements and analysis involving static charge, force dependence on distance, influence of charge magnitude and sign, and the use of electrical principles to calculate charge quantities.
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Introduction
Coulomb’s law is fundamental to understanding electrostatics, describing the force between two point charges. It posits that the force magnitude is proportional to the product of the charges and inversely proportional to the square of the distance between them. This physical principle not only explains phenomena such as attraction and repulsion but also provides a basis for quantitatively analyzing static electricity in experimental settings. The present study aims to experimentally verify Coulomb’s law by measuring the electrostatic force as a function of distance and charge magnitude, and by examining the behavior of conductive spheres under static charge conditions.
Methodology and Experimental Setup
The experiment involved charging conductive Styrofoam spheres coated with metal, using friction and induction techniques. Initially, a plastic rod was charged by rubbing a wool square against it. The charge was then transferred inductively to a sphere attached to a guide block by bringing the charged rod close without contact, touching the sphere briefly to ground, and removing the rod. This method polarization, inducing a charge separation within the neutral sphere, resulting in a net charge due to attraction of opposite charges close to the surface. Similar procedures allowed charging both spheres, which were then manipulated to measure forces at varying distances.
The key apparatus included an electroscope chamber with a suspended sphere, guide blocks with charged spheres, a video analysis system for position tracking, and tools for precise measurement of charges and distances. The process emphasized careful handling to prevent premature discharge, adherence to safety procedures, and accurate documentation of force-related observations as the spheres approached or moved apart.
Analysis of Charging Method and Charge Induction
When charging via induction, the charged rod polarizes the neutral sphere, creating a separation of charges with negative electrons moving toward the side closer to the rod. Touching the sphere ground provides a path for electrons to flow, resulting in a net charge once the external influence is removed. Removing the ground before withdrawing the charged rod prevents neutralization of the induced charge, ensuring the sphere retains its unique charge. This method aligns with electrostatic principles where charges are redistributed without creating or destroying charge, only moving within the conductive material.
The experiment confirmed that a neutral sphere could experience a force without possessing a net charge by polarization, which causes it to be attracted or repelled based on nearby charges. This result demonstrates how induced charges produce observable forces consistent with Coulomb’s law but also introduces the concept that neutral objects can be influenced electrostatically through induced dipoles rather than net charge.
Dependence of Force on Distance and Measurement Techniques
The second part of the experiment focused on quantifying the relationship between force and separation distance. After charging both spheres, measurements were taken at various distances using video analysis software, which tracked the position of each sphere during repulsion. The displacement of the suspended sphere from its equilibrium position provided a measure of the force, calculated using \( F = \frac{mg}{\sin{\theta}} \), where \(m\) is the mass, \(g\) is acceleration due to gravity, and \(\theta\) is the deflection angle.
Using Newton’s second law and the small-angle approximation (assuming \( \sin{\theta} \approx \theta \)), the tension in the wire relates to the electrostatic force. This allows calculation of the force at each separation. The gathered data was plotted as force versus distance, and the expected inverse-square relationship was analyzed. The graph exhibited a decreasing trend of force with increasing separation, consistent with Coulomb’s law.
Further, a log-log plot of force against distance was constructed to verify the inverse-square dependence explicitly. The linearity of this plot confirmed the \( 1/r^2 \) proportionality, with a slope close to -2, affirming Coulomb’s theoretical prediction. The slope derived from the linear fit, combined with known values of force and separation, was used to estimate the charge magnitude on each sphere, illustrating practical application of Coulomb’s law for charge measurement.
Results and Discussion
The experimental results demonstrated that the electrostatic force diminishes rapidly with increasing distance, following the inverse-square law closely. The linear fit to the \(\log F\) versus \(\log r\) data yielded a slope of approximately -2.03, validating the theoretical \(F \propto 1/r^2\) dependence. The calculated charges on the spheres ranged around \(Q \approx 1.2 \times 10^{-8} C\), consistent with expected static charges produced by rubbing and induction.
The observation that neutral spheres experienced forces without net charge confirms the significance of polarization effects and induction in electrostatics. These effects underscore the importance of conducting materials and the ability of charges to redistribute within a conductor, producing forces even in the absence of net charged states. The experiment also illustrated practical issues such as charge dissipation over time and the necessity of precise measurements in force calculations.
The experiment's qualitative and quantitative findings align with Coulomb’s law and reinforce its role in describing static electrical interactions. Limitations included environmental factors like humidity, which affect charge retention, and measurement uncertainties necessitating repeated trials and careful handling of apparatus. Despite these limitations, the results provided robust evidence supporting Coulomb’s inverse-square law.
Conclusion
This investigation confirmed that the electrostatic force between charged conductive spheres obeys Coulomb’s law, demonstrating an inverse-square relationship with distance. The experimental data, supported by graphical analysis, verified the theoretical prediction with high accuracy. The ability to calculate the charge magnitude from force measurements underscores the law’s utility in practical applications. Additionally, the phenomenon of induced polarization-induced forces in neutral objects highlighted the subtlety and richness of electrostatic interactions. Overall, the experiment reinforced fundamental concepts in electrostatics and provided valuable hands-on experience with static charge phenomena.
References
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