homework12

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