The discussion revolves around the electric field equations for a charged sphere, specifically seeking a single equation that describes the electric field both inside and outside the sphere, as well as at its surface. Participants explore the differences in the equations provided by sources like hyperphysics, which present separate equations for the electric field inside and outside the sphere.
Participants generally agree that there are two distinct equations for the electric field inside and outside the sphere. However, there is disagreement on whether a single equation can be formulated to encompass both regions, with some suggesting the possibility of an integral approach while others emphasize the inherent discontinuity.
The discussion highlights limitations related to the continuity of the electric field at the surface of the sphere and the challenges in defining a single equation that accurately describes the electric field across different regions.
There is just one equation. However, because the gradient is discontinuous across the surface, when we write the equation as an analytic function, it must be split into two regimes. If this bothers you, realize that if you were to try to find a single continuous function to describe the density rho both inside and outside the sphere, you would end up with the same problem: no way to do it.cefarix said:The equations are two though, one for the field inside, and separate one for the field outside. I suppose there is no way to directly combine these two equations. However can't we derive an equation which, I guess would be in integral form, summing up the flux through infinitesimal patches over the sphere's surface?