How to calculate electric field of arbitrary tetrahedron with uniform charge density at arbitrary point?
- 4 tetrahedron vertices
- total charge in Coulombs
- point at which I want to compute E field vector
The point can be outside or inside the tetrahedron. The charge density is uniform across tetrahedron volume (not surface!).
This is not a homework. I'm writing a simulation program to simulate electric fields around and inside an object defined by its 3D mesh. The field to calculate is of all the protons in an object. It is assumed they are uniformly spread across entire volume. Imagine protons field only as if you removed all valence electrons from the metal, so each atom would have +1e charge. I was thinking about subdividing the mesh to smaller chunks (tetrahedrons) and adding each tetrahedron fields at particular point.
I came up with a solution for the inner field part if outside field equation is known. The idea is to check if the point at which we want compute the field is inside the tetrahedron. If it's not then we compute field regularly, if it's inside then we choose a plane containing one tetrahedron's edge (or any two vertices) and that point. This plane will split the tetrahedron into two smaller ones. We then compute and add fields of both of them. In this case point can be considered to be outside of each smaller tetrahedron, or lying on their surfaces.