- #1
OliviaB
- 4
- 0
Apply the method of images to derive the solution
[tex]\displaystyle \phi(x,y,z) = \frac{z}{2 \pi} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} \frac{f(x_0, y_0)}{((x - x_0)^2 + (y - y_0)^2 + z^2)^{\frac{3}{2}}} dx_0 dy_0[/tex]
from
[tex]\displaystyle \bigtriangledown^2 \phi (x,y,z) = 0 [/tex]
[tex]\phi(x,y,0) = f(x,y)[/tex]
from the region [tex]- \infty < x < \infty, - \infty < y < \infty, 0 < z < \infty [/tex]
Its hard for me to start because I don't really understand the method of images.
[tex]\displaystyle \phi(x,y,z) = \frac{z}{2 \pi} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} \frac{f(x_0, y_0)}{((x - x_0)^2 + (y - y_0)^2 + z^2)^{\frac{3}{2}}} dx_0 dy_0[/tex]
from
[tex]\displaystyle \bigtriangledown^2 \phi (x,y,z) = 0 [/tex]
[tex]\phi(x,y,0) = f(x,y)[/tex]
from the region [tex]- \infty < x < \infty, - \infty < y < \infty, 0 < z < \infty [/tex]
Its hard for me to start because I don't really understand the method of images.