Charge Simulation Method of calculation of Electric Field
Q. Describe in brief the charge simulation method for estimation of Electric Field Intensity.
- It describes the surface charge present at the boundary of an electrode by fictitious , discrete charges in the interior of the electrode.
- Point, line or ring type charges are possible depending upon the geometry.
- The position and the type of simulation charges are to be determined first and then the magnitudes of the charges are calculated so that their combined effects satisfy the boundary conditions.
- The potential of the various types of charges are Φ (
) = P () Q where, P – is the potential coefficient dependent on location and type of charge Q – the charge or charge per unit length. For a point charge,
P (r) = 1/4π∈ r
- The potential is known at the contour points on the electrode. If the charge location is also specified, we can obtain the potential at the contour point K.
ΦK = N
Σ PK (k) Qi
I = 1
- Which leads to a matrix equation when extended to all contour points. The unknown charges can be determined by the inversion of [P]
[Φ] = [P] [Q]
- After solving this equation it is necessary to check whether the set of calculated charges produces the actual boundary conditions everywhere on the electrode surfaces.
- Charge simulation method for multi dielectric medium is more complicated than a single dielectric as under the influence of applied voltage the dipoles are realigned in a dielectric and it has the effect of producing a net surface charge on the dielectric.
- Therefore in addition to the electrodes each dielectric surface needs to be simulated by the discrete charges.
- The accuracy of simulation of multidielectric boundaries deteriorates when the dielectric boundary has a complex profile.
- The error of this method depends upon the type, number as well as the locations of the simulation charges, the locations of contour points and the complexity of the profile of electrodes and the dielectrics.