# Vol. 9

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2009-11-09

#### Introducing Fictitious Currents for Calculating Analytically the Electric Field in Cylindrical Capacitors

By Romain Ravaud, Guy Lemarquand, and Slobodan Babic
Progress In Electromagnetics Research M, Vol. 9, 139-150, 2009
doi:10.2528/PIERM09101509

## Abstract

The aim of this paper is to show the interest of using equivalence models for calculating the electric field produced by cylindrical capacitors with dielectrics. To do so, we use an equivalent model, based on the dual Maxwell's Equations for calculating the two electric field components created inside the capacitor and outside it. This equivalent model uses fictitious currents generating a electric vector potential that allows us to determine the electric field components in all points in space. The electric field produced by charge distributions as capacitor with dielectrics is generally determined by using the coulombian model. Indeed, it is well known that the electric field derives from a scalar potential. By using the Maxwell's equations, this scalar potential is in fact linked to the existence of charge distributions that are generally located on the faces of the capacitors. However, this last model does not allow us to obtain reduced analytical expressions since it involves the calculation of charge volume density appearing in the dielectric material for arcshaped cylindrical topologies. Consequently, it is interesting to look for another approach that gives analytical expressions with a lower computational cost. In this paper, we show that the use of fictitious currents instead of charges allow us to obtain 3D analytical reduced expressions with a lower computational cost. This analytical approach is compared to the coulombian model for showing the equivalence between the two approaches.

## Citation

Romain Ravaud, Guy Lemarquand, and Slobodan Babic, "Introducing Fictitious Currents for Calculating Analytically the Electric Field in Cylindrical Capacitors," Progress In Electromagnetics Research M, Vol. 9, 139-150, 2009.
doi:10.2528/PIERM09101509
http://www.jpier.org/PIERM/pier.php?paper=09101509

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