Task01
Exercise 5.4 : Investigate how the magnitude of the fringing field of the capacitor,that is,the electric field outside the central region of the capcitor in Figure 5.6,varies as a function of plate separation.
Abstract
For Laplace's equation:
we use relaxation method that is convenient dealing with the class of PDEs know as elliptical eauations (Laplace's equation is included) to slove it.
Background
we rewrite Laplace's equation in finite-difference form:
for a two-dinmensional problem
Solution : the field of a parallel plate capacitor
Jacobi method :
in this method,only the old values of the potential are used to compute the values in the next iteration.
SOR method :
this method can accelerate the convergence of the program effetively.
separation=60:
separation=100:
separation=160:
Conclusion
from the plot above,we can observe that when the plate separation goes larger,the voltages in fringing field become intensive,that means the electric field intensity in fringing area is larger.
Reference
Computational Physics : Second Edition
Code from perfect Wuyuqiao
