The attraction field of a thin spherical shell, Fig

Applying again the Gauss s formula and taking into account the spherical symmetry, we find that inside the shell, R a, the field is absent, while outside, R ai, it behaves as a point source situated at the origin. Thus, we have 

We see that a summation of fields of elementary masses outside of the shell produces the same result as a point source, placed at the center of the shell. This is the second example of such equivalence, and again it is an exception. Consider a spherical surface S with radius R — a + r a2. Then, the radial component inside 

The behavior of g as a function of R is shown in Fig. 1.12c, and, of course, it is a continuous function. Now let us mentally decrease the thickness h and increase the volume density so that the mass remains the same. In such a way we arrive at a distribution of masses with a surface density, and this replacement does not change the field outside the shell, but it leads to a discontinuity of the field at the surface masses. It is instructive to demonstrate why the field inside the shell, R a, is zero. Let us take any point p, Fig. 1.12d, and form an elementary cone with its apex at this point. The lateral surface of the cone intersects the shell and generates inside two elementary surfaces dS and dS2- By definition we have  

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