Actually my question comes from Gauss law which says charges outside a closed surface, doesn't effect on the whole electric flux of the surface.

The reason of that is that the solid angle of a closed surface while measuring it from outside of the surface, is zero. ( on the other hand, the solid angle of a closed surface from inside the closed surface is $4\pi$)

My question is why solid angle of a closed surface from exterior is zero? Please don't use Stokes' theorem!

  • $\begingroup$ Please don't put the question only in the title, but repeat it in the body and elaborate on it. It is currently unclear what you're asking - what do you mean by "solid angle of a surface", and what has Gauß' law to do with it being zero outside the surface? $\endgroup$ – ACuriousMind Apr 25 '17 at 10:49
  • $\begingroup$ Sir, I meant that we can talk about Gauss law by using this fact, which the solid angle of a closed surface is zero when you are measuring it from outside of it. $\endgroup$ – David 2000 Apr 25 '17 at 12:58

As viewed from a point outside the surface, the closed surface has a far side and a near side. For example, for a cube there is a front face and a back face.

If there were a point charge situated where the viewer is, the flux from this charge goes into the enclosed volume across one surface and out of the enclosed volume across the other face. The total flux into or out of the volume is zero. Likewise when measuring solid angle the angle subtended by one of these surfaces is taken as being +ve and that subtended by the other is -ve. The front and back faces subtend the same angle, but these angles add up to zero.


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