EQS Solution with Uniformly Polarized Sphere

Editors：許正乾、劉育宗、曾富群

Adviser：江簡富 教授

    Denote the potentials inside and outside of the sphere as Φ_i  and Φ_o, respectively. The boundary conditions require that  Φ_o− Φ_i = 0 and −ε_o(∂Φ_o /∂ r) + ε_o(∂Φ_i/∂r) = P_ocosθ. Physical consideration also demands that Φ_o (r→∞)=0, and  Φ_i(r = 0) is finite. The functional form of surface polarization charge density and the physical consideration suggest the forms of potential distributions as

and

      

Furthermore, we can find the E_o and E_i from Φ_o and Φ_i. Thus,

and

(1) Potential Distribution

(2) Electric Field Distribution