Hi. I'm trying to find out a specific solution (in my case, the electric potential, V) of Laplace equation by using Mathematica but things just don't go so well.
Gotta remind that I'm completely new to this program tho
The situation is that two circular probes are settled on a flat plane, 2V circular probe of radius 2 centered at (-10, 0), -2V circular probe of radius 2 centered at (10, 0)
so I'd like to set the initial conditions for this situation to
- V=0 for sides of Rectangular[{-100, -100}, {100, 100}] (since the potential would approximately reach 0 at such distance)
- V=2 for circumference and inside of Disk[{-10, 0}, 2]
- V=-2 for circumference and inside of Disk[{10, 0}, 2]
I tried to find the solution of Laplace equation applying these initial conditions using NDSolve function,
sol=V[x,y]/. NDSolve[{D[V[x,y],x,x]+D[V[x,y],y,y]==0,
V[100, y]==0, V[-100, y]==0, V[x, 100]==0, V[x, -100]==0,
*initial condition 2*, *initial condition 3*}, V, {x, -100, 100}, {y, -100, 100}]
As you can see above, I failed to figure out expressing initial condition 2 and 3 as a code in Mathematica. It would be grateful to get help to figure it out.