nilbuwa
Sep14-11, 07:40 PM
Hi Everyone,
I am trying to solve the partial differential equation given below:
\Delta^2\phi(x,y,z)=\frac{qf(x,y,z)}{\epsilon}
where f(x,y,z)=1 at one point and zero elsewhere.
This is the poisons equation for a point charge inside a conducting box.
Can this be solved using the variable separable method?
When I work through it I get:
\frac{1}{X(x)}\frac{d^2X(x)}{dx^2}+\frac{1}{Y(y)} \frac{d^2Y(y)}{dy^2}+\frac{1}{Z(z)}\frac{d^2Z(z)}{ dz^2}=\frac{qf(x,y,z)}{\epsilon X(x)Y(y)Z(z)}
If this cannot be solved using this method. What others methods can I use. If some one can give me a reference I am thankful.
I am trying to solve the partial differential equation given below:
\Delta^2\phi(x,y,z)=\frac{qf(x,y,z)}{\epsilon}
where f(x,y,z)=1 at one point and zero elsewhere.
This is the poisons equation for a point charge inside a conducting box.
Can this be solved using the variable separable method?
When I work through it I get:
\frac{1}{X(x)}\frac{d^2X(x)}{dx^2}+\frac{1}{Y(y)} \frac{d^2Y(y)}{dy^2}+\frac{1}{Z(z)}\frac{d^2Z(z)}{ dz^2}=\frac{qf(x,y,z)}{\epsilon X(x)Y(y)Z(z)}
If this cannot be solved using this method. What others methods can I use. If some one can give me a reference I am thankful.