for the electric potential Φ: where ℜ 3 is the euclidian 3-dimensional space and Σ is the surface of the particle. The derivatives are taken with respect to the normal vector n to the surface Σ. Due to the mismatch between the polarization inside and outside the object, electric charges accumulate at the interface Σ and create an electric potential which counteracts the uniform electric field stimulus. The solution of the above Laplace problem (3) is therefore formally given by The single layer charge distribution µ induced by the normalized electric field is a solution of the following BIE, obtained by inserting solution (4) in equations (3) Here the parameter λ = ( ε$_{1}$ − ε$_{0}$ ) / ( ε$_{1}$ + ε$_{0}$ ) isolates all the information regarding the dielectric properties for this problem. On using the linear response operator M that acts on the Hilbert space of integrable functions on the surface Σ, the integral equation (5) is written as The integral operator (6) is the electric field generated by the single layer charge distribution µ along the normal to the surface. It encodes the geometric information and has several interesting properties [13–15]. Its spectrum is discrete and it is not difficult to show that all of its eigenvalues are bounded by the [-1/2, 1/2] interval. Although non-symmetric, the operator (6) has real non-degenerate eigenvalues. The eigenvectors are biorthogonal, i. e., 5 ΔΦ ( x ) = 0 , x ∈ ℜ $^{3}$\ Σ Φ | + = Φ | − , x ∈ Σ ε$_{0}$ ∂ Φ ∂ n ∣ + = ε$_{1}$ ∂ Φ ∂ n ∣ − , x ∈ Σ Φ → − x · N , | x | → ∞ (3) Φ( x ) = − x · N + 1 4 π ∫ Σ µ ( y ) | x − y | d Σ( y ) (4) µ ( x ) 2 λ − 1 4 π ∫ Σ µ ( y ) n ( x ) · ( x − y ) | x − y | 3 d Σ( y ) = n ( x ) · N (5) M [ µ ] = 1 4 π ∫ Σ µ ( y ) n ( x ) · ( x − y ) | x − y | 3 d Σ( y ) , (6) (1 / (2 λ ) − M ) µ = n · N . (7)