Computer Algebra Recipes

234 CHAPTER 5. LINEAR PDE MODELS. PART 1
> phi:=subs(fr=sqrt(x^2+y^2),cos(theta)=x/sqrt(x^2+y^2),
sin(theta)=y/sqrt(x^2+y^2)g,phi):
He then creates a piecewise potential function © equal to Á for 100 · x2 + y2 ·
400 and zero otherwise. (The © output is suppressed here.)
> Phi:=piecewise(100implicitplot(fPhi=5*ig,x=-20..20,y=-20..20,
scaling=constrained,grid=[100,100]):
The sequence of constant-potential plots is then displayed for i = ¡6 to+6,
the result being shown in Figure 5.8.
> display(fseq(F(i),i=-6..6)g);
20
y
10
–20 –10 10 20
x
–10
–20
Figure 5.8: Equipotential lines for the circular annulus.
Although, he hasn't bothered to label the equipotential lines, Benny feels that
the plot already conveys a better sense of the equipotentials than could be
gained by staring at the formula, simple as it is. He has left the labeling of the
equipotentials for you to carry out as a problem.
PROBLEMS:
Problem 5-15: Labeling of equipotential lines
Using the textplot command, add appropriate potential values to Figure 5.8
so that the equipotential lines are clearly identi¯ed.