A conducting ball in an axial electric field
  We describe the distribution of a charge, the electric moments of arbitrary order and the force acting on a conducting ball on the axis of the axial electric field. We determine the full charge and the dipole moments of the first order for a conducting ball in an arbitrary inhomogeneous harmonic electric field. All statements are formulated in the form of theorems with proofs basing on properties of the matrix of moments of the Legendre polynomials. The analysis and proof of these properties are presented in Appendix. 
Alexander Savchenko
math-ph math.MP