- #1
Anabelle37
- 39
- 0
Homework Statement
Consider the transformation: w = i[(1-z)/1+z)]
Find the electrostatic potential V in the space enclosed by the half circle x^2 + y^2 = 1, y =>0
and the line y = 0 when V = 0 on the circular boundary and V = 1 on the line segment [-1,1].
Homework Equations
w = u + iv
z = x + iy
The Attempt at a Solution
I solved for u and v by substituting w and z into the transformation.
I got:
u=2y/(x^2+2x+y^2+1)
v=(1-x^2-y^2)/(x^2+2x+y^2+1)
I found the question on this website on the last 2 pages:
http://www.math.okstate.edu/~binegar/5233-S96/5233-l13.pdf
I got the u and v the other way around than what they did but I think I'm right?
Also I don't know how they got the expression for V(u,v) to solve for the electrostatic potential.
I know the boundary conditions are V(u,0)=1 and V(0,v)=0
PLEASE HELP!