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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