I'm trying to find the flux(divergence) via vector surface integrals out out of a solid region that is part of a ball given by $1\leq r \leq 4$ using the inverse square field. I'm wondering whether by symmetry, the flux out of such a solid region is the flux out of a ball of radius four minus the flux out of a ball of radius one.
2026-03-28 07:05:03.1774681503
Surface Integral and Symmetry
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Yes the flux out of such a solid region is the flux out of a ball of radius four minus the flux out of a ball of radius one because the surface of the solid is the union of two spheres oriented differently which explains the negative sign in computation.