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Electric potential of a point charge in multilayered dielectrics evaluated from Hankel transform

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Abstract

Electric potential of a point charge embedded in a three-layered dielectric system with infinite planar interfaces is determined. Using the technique of Hankel transform, the electric potentials in all domains are obtained in closed form. Nondimensionalization of the solution reduces the governing parameters into three scalars: a normalized charge location and two dielectric constant ratios. Numerical parametric study reveals interesting, coupled influences of these parameters on the distribution of electric potential. Due to the linear nature of the electrostatic problem, the solution here can be extended to similar multilayered dielectric systems with a distribution of charges.

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References

  1. Pan M-J, Randall CA (2010) A brief introduction to ceramic capacitors. Electr Insul Mag IEEE 26:44–50

    Article  Google Scholar 

  2. Jain P, Rymaszewski EJ (2002) Embedded thin film capacitors-theoretical limits. IEEE Trans Adv Packag 25:454–458

    Article  Google Scholar 

  3. Wei C, Harrington RF, Mautz JR, Sarkar TK (1984) Multiconductor transmission lines in multilayered dielectric media. IEEE Trans Microw Theory Tech 32:705–710

    Article  Google Scholar 

  4. Crampagne R, Ahmadpanah M, Guiraud J-L (1978) A simple method for determining the Greens function for a large class of MIC lines having multilayered dielectric structures. Microw Theory Tech 26:82–87

    Article  Google Scholar 

  5. Silvester P (1968) TEM wave properties of microstrip transmission lines. Electr Eng Proc Inst 115:43–48

    Article  Google Scholar 

  6. Smith CE, Chang R-S (1980) Microstrip transmission line with finite-width dielectric. IEEE Trans Microw Theory Tech MTT 28:90–94

    Article  Google Scholar 

  7. Brrmann K, Burger K, Jagota A, Bennewitz R (2012) Discharge during detachment of micro-structured PDMS sheds light on the role of electrostatics in adhesion. J Adhes 88:589–607

    Article  Google Scholar 

  8. Wan K-T, Smith DT, Lawn BR (1992) Fracture and contact adhesion energies of mica-mica, silica-silica, and mica-silica interfaces in dry and moist atmospheres. J Am Ceram Soc 75:667–676

    Article  Google Scholar 

  9. Pumplin J (1969) Application of Sommerfeld-Watson transformation to an electrostatics problem. Am J Phys 37:737

    Article  Google Scholar 

  10. Pronic O, Markovic V, Milovanovic B (2001) Numerically efficient Greens function for planar structures on multilayered dielectric in cylindrical enclosure. COMPEL Int J Comput Math Electr Electron Eng 20:1055–1070

    Article  MathSciNet  MATH  Google Scholar 

  11. Sten JC-E, Ilmoniemi R (1994) Image theory for a point charge inside a layered dielectric sphere. Arch Elektrotech 77:327–335

    Article  Google Scholar 

  12. Heubrandtner T, Schnizer B, Lippmann C, Riegler W (2002) Static electric fields in an infinite plane condenser with one or three homogeneous layers. Nucl Inst Methods Phys Res Sect A 489:439–443

    Article  Google Scholar 

  13. Xue C, Deng S (2015) Coulomb Greens function and image potential near a planar diffuse interface, revisited. Comput Phys Commun 184:51–59

    Article  MathSciNet  MATH  Google Scholar 

  14. Lin H, Xu Z, Tang H, Cai W (2012) Image approximations to electrostatic potentials in layered electrolytes/dielectrics and an ion-channel model. J Sci Comput 53:249–267

    Article  MathSciNet  MATH  Google Scholar 

  15. Barrera RG (1978) Point charge in a three-dielectric medium with planar interfaces. Am J Phys 46:1172

    Article  Google Scholar 

  16. Pont FM, Serra P (2015) Comment on Point charge in a three-dielectric medium with planar interfaces [Am. J. Phys. 46, 1172–1179 (1978)]. Am J Phys 83:475–476

    Article  Google Scholar 

  17. Bakr AA, Fenner RT (1983) Use of the Hankel transform in boundary integral methods for axisymmetric problems. Int J Numer Methods Eng 19:1765–1769

    Article  MATH  Google Scholar 

  18. Ai ZY, Yue ZQ, Tham LG, Yang M (2002) Extended Sneddon and Muki solutions for multilayered elastic materials. Int J Eng Sci 40:1453–1483

    Article  MathSciNet  MATH  Google Scholar 

  19. Harding J, Sneddon IN (1945) The elastic stress produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch. Proc Camb Phil Soc 41:16–26

    Article  MATH  Google Scholar 

  20. Erdelyi A (ed) (1954) Tables of integral transforms Bateman manuscript project, vol II. McGraw Hill, New York

    Google Scholar 

  21. Jackson JD (1999) Classical electrodynamics. Wiley, New York

    MATH  Google Scholar 

  22. Farrar A, Adams AT (1974) Multilayer microstrip transmission lines (Short Papers). IEEE Trans Microw Theory Tech 22:889–891

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge the financial support from the Natural Science and Engineering Research Council (NSERC).

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Alberta, Edmonton, T6G 1H9, Canada

    Hasib Ibne Rahman & Tian Tang

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  1. Hasib Ibne Rahman
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  2. Tian Tang
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Correspondence to Tian Tang.

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Rahman, H.I., Tang, T. Electric potential of a point charge in multilayered dielectrics evaluated from Hankel transform. J Eng Math 110, 63–73 (2018). https://doi.org/10.1007/s10665-017-9929-3

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  • DOI: https://doi.org/10.1007/s10665-017-9929-3

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