Vol. 107
Latest Volume
All Volumes
PIERL 121 [2024] PIERL 120 [2024] PIERL 119 [2024] PIERL 118 [2024] PIERL 117 [2024] PIERL 116 [2024] PIERL 115 [2024] PIERL 114 [2023] PIERL 113 [2023] PIERL 112 [2023] PIERL 111 [2023] PIERL 110 [2023] PIERL 109 [2023] PIERL 108 [2023] PIERL 107 [2022] PIERL 106 [2022] PIERL 105 [2022] PIERL 104 [2022] PIERL 103 [2022] PIERL 102 [2022] PIERL 101 [2021] PIERL 100 [2021] PIERL 99 [2021] PIERL 98 [2021] PIERL 97 [2021] PIERL 96 [2021] PIERL 95 [2021] PIERL 94 [2020] PIERL 93 [2020] PIERL 92 [2020] PIERL 91 [2020] PIERL 90 [2020] PIERL 89 [2020] PIERL 88 [2020] PIERL 87 [2019] PIERL 86 [2019] PIERL 85 [2019] PIERL 84 [2019] PIERL 83 [2019] PIERL 82 [2019] PIERL 81 [2019] PIERL 80 [2018] PIERL 79 [2018] PIERL 78 [2018] PIERL 77 [2018] PIERL 76 [2018] PIERL 75 [2018] PIERL 74 [2018] PIERL 73 [2018] PIERL 72 [2018] PIERL 71 [2017] PIERL 70 [2017] PIERL 69 [2017] PIERL 68 [2017] PIERL 67 [2017] PIERL 66 [2017] PIERL 65 [2017] PIERL 64 [2016] PIERL 63 [2016] PIERL 62 [2016] PIERL 61 [2016] PIERL 60 [2016] PIERL 59 [2016] PIERL 58 [2016] PIERL 57 [2015] PIERL 56 [2015] PIERL 55 [2015] PIERL 54 [2015] PIERL 53 [2015] PIERL 52 [2015] PIERL 51 [2015] PIERL 50 [2014] PIERL 49 [2014] PIERL 48 [2014] PIERL 47 [2014] PIERL 46 [2014] PIERL 45 [2014] PIERL 44 [2014] PIERL 43 [2013] PIERL 42 [2013] PIERL 41 [2013] PIERL 40 [2013] PIERL 39 [2013] PIERL 38 [2013] PIERL 37 [2013] PIERL 36 [2013] PIERL 35 [2012] PIERL 34 [2012] PIERL 33 [2012] PIERL 32 [2012] PIERL 31 [2012] PIERL 30 [2012] PIERL 29 [2012] PIERL 28 [2012] PIERL 27 [2011] PIERL 26 [2011] PIERL 25 [2011] PIERL 24 [2011] PIERL 23 [2011] PIERL 22 [2011] PIERL 21 [2011] PIERL 20 [2011] PIERL 19 [2010] PIERL 18 [2010] PIERL 17 [2010] PIERL 16 [2010] PIERL 15 [2010] PIERL 14 [2010] PIERL 13 [2010] PIERL 12 [2009] PIERL 11 [2009] PIERL 10 [2009] PIERL 9 [2009] PIERL 8 [2009] PIERL 7 [2009] PIERL 6 [2009] PIERL 5 [2008] PIERL 4 [2008] PIERL 3 [2008] PIERL 2 [2008] PIERL 1 [2008]
2022-11-08
On the Electrostatic Interaction Between Point Charges Due to Dielectrical Shielding
By
Progress In Electromagnetics Research Letters, Vol. 107, 111-118, 2022
Abstract
How will the electrostatic interaction between two point charges change if they are shielded from the other by a dielectrical slab? While the physical setting of this electromagnetic problem is relatively simple, it is easy to be wronged, and the correct solution is surprisingly complicated. Here we will show a general answer using the method of images, in which the electrical field is not found by solving the Poisson's equation but by superposing an infinite number of image charges to recurrently satisfy all interfaces' boundary conditions. We also obtain analytical and algebraic results in some special cases.
Supplementary Information
Citation
Long T. Nguyen, Tuan K. Do, Duy V. Nguyen, and Trung V. Phan, "On the Electrostatic Interaction Between Point Charges Due to Dielectrical Shielding," Progress In Electromagnetics Research Letters, Vol. 107, 111-118, 2022.
doi:10.2528/PIERL22071401
References

1. Celozzi, S., R. Araneo, and G. Lovat, Electromagnetic Shielding, John Wiley & Sons, 2008.
doi:10.1002/9780470268483

2. Barcellona, P., R. Bennett, and S. Y. Buhmann, "Manipulating the Coulomb interaction: A Green's function perspective," Journal of Physics Communications, Vol. 2, No. 3, 035027, 2018.
doi:10.1088/2399-6528/aaa70a

3. Purcell, E. M. and D. J. Morin, Electricity and Magnetism, Cambridge University Press, 2013.
doi:10.1017/CBO9781139012973

4. Landau, L. D., E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, Vol. 8, Elsevier, 2013.

5. Stratton, J. A., Electromagnetic Theory, Vol. 33, John Wiley & Sons, 2007.

6. Hammond, P., "Electric and magnetic images," Proceedings of the IEE --- Part C: Monographs, Vol. 107, 306, 1960.
doi:10.1049/pi-c.1960.0047

7. Jackson, J. D., Classical Electrodynamics, Vol. 31999, Wiley, New York, 1977.

8. Lindell, I. V., "Electrostatic image theory for the dielectric sphere," Radio Science, Vol. 27, No. 1, 1-8, 1992.
doi:10.1029/91RS02255

9. Lindell, I. V., M. E. Ermutlu, and A. H. Sihvola, "Electrostatic image theory for layered dielectric sphere," IEE Proceedings H (Microwaves, Antennas and Propagation), Vol. 139, No. 2, 186-192, 1992.
doi:10.1049/ip-h-2.1992.0035

10. Nikoshkinen, K. I. and I. V. Lindell, "Image solution for Poisson's equation in wedge geometry," IEEE Transactions on Antennas and Propagation, Vol. 43, No. 2, 179-187, 1995.
doi:10.1109/8.366380

11. Johan, C.-E. S. and I. V. Lindell, "Electrostatic image theory for the dielectric sphere with an internal source," Microwave and Optical Technology Letters, Vol. 5, No. 11, 597-602, 1992.
doi:10.1002/mop.4650051115

12. Lindell, I. V. and I. N. Keijo, "Electrostatic image theory for the dielectric prolate spheroid," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 8, 1075-1096, 2001.
doi:10.1163/156939301X00436

13. Sometani, T., "Image method for a dielectric plate and a point charge," European Journal of Physics, Vol. 21, No. 6, 549, 2000.
doi:10.1088/0143-0807/21/6/305

14. Cartier, P. E., B. Julia, P. Moussa, and P. Vanhove, Frontiers in Number Theory, Physics, and Geometry II: on Conformal Field Theories, Discrete Groups and Renormalization, Vol. 2, Springer Science & Business Media, 2007.

15. Loxton, J., "Special values of the dilogarithm function," Acta Arithmetica, Vol. 43, No. 2, 155-166, 1984.
doi:10.4064/aa-43-2-155-166

16. Bossa, G. V. and S. May, "Integral representation of electrostatic interactions inside a lipid membrane," Molecules, Vol. 25, No. 17, 3824, 2020.
doi:10.3390/molecules25173824