Nonretarded limit

PROBLEM LI.I3 Working in the nonretarded limit and in the limit of close approach / Ri, R2, compare the free energy of interaction per unit area of planar facing surfaces, Gim/2m(0, with the free energy per interaction, that is, the integral Gss(/ Ri, R2) of / ss(/ Ri, R2). In particular, show that... 

Magnetic (In the nonretarded limit, with the finite velocity of light neglected, An... 

Table S.13. Two point particles in a vapor, near or touching a substrate (nonretarded limit)...

Note Nonretarded limit, rn - 0, integral dominated by large p where Sj = sz = p... 

Nonretarded limit When the velocity of light is imagined infinite, all r - 0, a... 

Small differences in e s and //s, nonretarded limit In the further limit at which c -+... 

Dielectric properties need not change in sharp steps. Recognizing the possibility that they can change continuously reveals qualitatively new forms of force versus separation. Imagine, for example, regions where we can write e = e(z). In the nonretarded limit, electric waves satisfy an equation... 

L. Bergstrom, "Hamaker constants of inorganic materials," Adv. Colloid Interface Sci., 70, 125-69 (1997), together with a brief tutorial on computation, contains a useful collection of interaction coefficients in the nonretarded limit. 

Equation (5.23) relates the intensities of the outgoing magnetic and electric modes to those of the ingoing modes in a similar manner to the scalar equations (4.42), (4.52), and (4.69) in the nonretarded limit. 

There is a symmetric coupling between electric and magnetic modes. In the nonretarded limit, when c approaches infinity, we find that the second terms in Eqs. (5.27), (5.28), and (5.30) vanish and the magnetic and electric modes respond to the changes /Xj<- /x and respectively. 

The convergence of all multipole interaction terms in Eq. (6.8) is guaranteed by the decrease of the multipole susceptibilities A X, j), on the one hand, and by the decrease of the phase shift factor exp(-2C), iC = Kr2i, with increasing imaginary frequency, on the other hand. At small separations d = r2i —Ri —i 2 of the spheres considered we find that the multipole susceptibilities decrease more rapidly than the phase shift factor. Neglecting the latter, we obtain the nonretarded limit. At large separations r2i of the spheres under consideration, when the phase... 

The reduction of the general dispersion function G (o,ii) given by the determinant (6.6) to the nonretarded limit is achieved by using... 

By considering the nonretarded limit of Eqs. (6.15), (6.16) we readily reobtain Eqs. (4.57)-(4.59). The modified Bessel function of the second kind equals the Bessel function of the third kind except... 

By taking the nonretarded limit of the electric multipole susceptibility A22 m,j), we recover the electrostatic multipole susceptibility (7.48) except for the factor l) (m- -l) /pm) (2m+1) , which... 

---