A conducting sphere of radius (ra) is surrounded by a charged spherical shell of radius (rb). The inner shell is held at a constant potential, Po while the outer shell has a surface charge density, (0,0), given by... (0,0)=sin(20) cos(6) (19) The Potential, (7,0,0) satisfies the Laplace Equation in Spherical Coordinates in the following regions, such that... a<r<b and r>b Solution for a <r<b: Assuming axially symmetry s.t. m = 0 (1,0,0)=A+Bir (1+1)] Pi (cos(0) Solution for r> b: Assuming axially symmetry s.t. m = 0 42(1,0,0) Cr(+1)]P(cos(0) 1=0 Solution for σ in terms of a sum.... 0 m=1 σ(0, 1) = ΣΣ στ7" (θ, 4) 1-0 m-1 (0,0)-02sin(20) cos() ...within these two regions, the potential is constrained by the following boundary conditions.... (i) (a,0,0)=0 (ii) (0,0,0)=0 (iii) (r,0,0) is continuous at r = b 04 = Dr which has (iv) From Gauss' Law, the radial electric field Er a discontinuity at rb, such that.... ЭФ1+6 σ Or -b (20) d) Conditions (iii) and (iv) must apply for each term in the sum over 1 and m. Apply them term by term at r = b to obtain the complete solution to the problem.