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Analytical model for the formation of electric fields in parallel-plate capacitors

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In this study, we propose an analytical model to elucidate the formation of electric fields between two parallel conducting plates. Using nine Gaussian surfaces, we investigated the charge redistributions and electric fields formed by parallel conducting plates when two charged plates get close together. The electric charges are redistributed via a new electrostatic equilibrium to create the electric field of each plates. As a result, the electric field start from + electrode plate to - electrode plate via inducing a new electrostatic equilibrium, implying that the application of Gaussian surfaces to only one of the electrodes of parallel-plate capacitors is deserved. The results will help undergraduate students understand the charge redistribution and the electric field formation in parallel-plate capacitors in a reasonable manner.

Abstract

In this study, we propose an analytical model to elucidate the formation of electric fields between two parallel conducting plates. Using nine Gaussian surfaces, we investigated the charge redistributions and electric fields formed by parallel conducting plates when two charged plates get close together. The electric charges are redistributed via a new electrostatic equilibrium to create the electric field of each plates. As a result, the electric field start from + electrode plate to - electrode plate via inducing a new electrostatic equilibrium, implying that the application of Gaussian surfaces to only one of the electrodes of parallel-plate capacitors is deserved. The results will help undergraduate students understand the charge redistribution and the electric field formation in parallel-plate capacitors in a reasonable manner.

참고문헌 (11)

  1. "Field between the plates of a parallel plate capacitor using Gauss's Law" (2014)[URL]
  2. Grove, T. T., "Determining dielectric constants using a parallel plate capacitor", Am. J. Phys, 73(1), pp.52~56 (2004)
  3. Halliday, D., "Principles of Physics" (2014), John Wiley & Sons
  4. Invchenko, V., "On the applicability limits of some ‘infinite’ models in the course of electricity and magnetism", Revista Brasileira de Ensino de Física, 43, pp.e20210108~ (2021)
  5. Kinght, R. D., "Physics for Scientist and Engineers" (2017), Pearson Education
  6. "What is the electric field in a parallel plate capacitor ?" (2013)[URL]
  7. Radivojević, V. M., "Measuring the dielectric constant of paper using a parallel plate capacitor", Int. J. Electr. Comput. Eng. Syst, 9(1), pp.1~10 (2018)
  8. Serway, R. A., "College Physics" (2017), Cengage Learning
  9. Tipler, P. A., "Physics for Scientists and Engineers with Modern Physics" (2004), W. H. Freeman
  10. Tipler, P. A., "Physics for Scientists and Engineers with Modern Physics" (2008), W. H. Freeman
  11. Wolfson, R., "Physics for Scientist and Engineers" (2017), Addison Wesley

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