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ION–ION INTERACTIONS  275










                     Fig. 3.29. At 0.1 N, the thickness of the ion cloud is only
                     10 times the radius of the central ion.


         invoked. The linearized P–B equation involved neither the point-charge approxima-
         tion nor any considerations of the dimensions of the ions. Hence, the basic differential
         equation







         and its general solution, i.e.,







         can be taken as the basis for the generalization of the theory for finite-sized ions.
             As before  (Section 3.3.7),  the  integration constant B must  be  zero  because
         otherwise one  cannot satisfy the  requirement of  physical  sense  that, as
               Hence, Eq. (3.28) reduces to







             In evaluating the constant A, a procedure different from that used after (3.29) is
         adopted. The charge dq in any particular spherical shell (of thickness dr) situated at a
         distance r from the origin is, as argued earlier,






         The charge density  is obtained thus
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