Nanosphere in the Quasi-Static Approximation

This is thus an electrostatic problem, which requires the solution of the the Laplace equation for the electrostatic potential (in the Fourier domain)  

It can be seen that this problem has an azimuthal symmetry and the general solution is of the form [1]  

From these two conditions we obtain that Ai = Ci = Q for I 1, and calculating of the remaining coefficients A] and C / we obtain the final expression for the potentials  

190) indicates that o t is given the superposition of the external applied potential and that of a dipole located at the particle center. We can simplify o t by introducing the dipole moment fisph of the sphere as 

The external applied field induces a dipole moment inside the sphere of a magnitude proportional to Eq. Thus we can introduce the effective polarizability of the sphere asph(o)), defined via jisph = Sout sph ( w)Eo, 

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