- #1
yosimba2000
- 206
- 9
So by definition, divergence means the ∫Flux Thru Differential Surfaces / ∫Differential Volume. So basically this just means we're calculating the fluxes divided by some factor, and Maxwell's first equation claims that ∇⋅E = q / εo is always true regardless of the shape of the surrounding surface.
I'm not understanding why this is true and how one could have figured this out. For a sphere it's clear that this is true, but how is it possible to generalize over all surfaces? I'm just thinking out loud here, but maybe all possible volumes are somehow the same as spheres, which is why they act the same? I realize that it's a law, so most likely it's just a postulate taken to be true, but is there a proof?
I'm not understanding why this is true and how one could have figured this out. For a sphere it's clear that this is true, but how is it possible to generalize over all surfaces? I'm just thinking out loud here, but maybe all possible volumes are somehow the same as spheres, which is why they act the same? I realize that it's a law, so most likely it's just a postulate taken to be true, but is there a proof?