Electric field outside of charged sphere

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Case 1. You have a sphere with Radius R and middle point X with the charge Q. The charge is equally distributed over the sphere.
for E(X,r) = 0 for r_1 < R, E inside the sphere is 0.
If r_2 > R then E ≠ 0 ; but let's say E(X,r_2) := w

If you put all the charge of the sphere into X then, it would still be E(X,r_2) = w
Why is that so? I could imagine that, if you had r_1 << R, but I found it first without the special case that R a lot larger than r_1
Where can I get information about that?

Case 2. Now the charge is no longer equally distributed over the sphere. Then E(X,r_1) is no longer 0. But what happens with E(X, r_2) ?
My guess is, that E = w, because in case 1 it didn't matter, if you viewed the sphere as a sphere or as a point. However I can't say for sure.

Can someone plz help me?
 

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vanhees71
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You have to solve the electrostatic problems including the boundary conditions (at the surface, tangential components of the electric field must be continuous while normal components can jump if there is a surface charge).

Further you need to know, whether the sphere is conducting or not. This can, however only be the case for the two scenarios in case 1. Then you have the condition that the tangential components of the E-field must not only be continuous but also vanish along the surface, because statics demands that there must not be currents.
 

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