Before revision: Start with Maxwell's equations away from the sources (Gaussian units): Using Stokes' theorem in one can conclude from the first of the above equations that for any domain in with a piecewise smooth boundary the following is true: where is the projection of the outward unit normal of onto the 3D slice , and is the volume 3-form on .
After revision: (3-dimensional)Start with Maxwell's equations away from the sources (Gaussian units): Using Stokes' theorem in one can conclude from the first of the above equations that for any domain in with a piecewise smooth boundary the following is true: where is the projection of the outward unit normal of onto the 3D slice , and is the volume 3-form on .