Induced charge of spherical dust particle on plasma-facing wall in non-uniform electric field

Induced charge of a spherical dust particle on a plasma-facing wall was investigated analytically, where non-uniform electric field was applied externally. The one-dimensional non-uniform electrostatic potential was approximated by the polynomial of the normal coordinate toward the wall. The bipolar coordinate was introduced to solve the Laplace equation of the induced electrostatic potential. The boundary condition at the dust surface determines the unknown coefficients of the general solution of the Laplace equation for the induced potential. From the obtained potential the surface induced charge can be calculated. This result allows estimating the effect of the surrounding plasma, which shields the induced charge.