Question

Please help solve. There is a 2nd page of steps attached after the question of how this problem should be solved. Use it as a guide to help solve the problem

Answer 1

In Fig. we divide it into 4 parts Take radius r = a Since sigma Er = -sigma dV/dr at the outer boundary, the boundary condition at r = a can be written dV1 Vertical-bar r = a)/dr = 0 dV2 Vertical-bar r = a)/dr = dV3(r = a)/dr = dV4^(r = a)/dr = V0 Like wise, the condition that sigma E straightphi = -sigma dV/d straightphi is continuous at the boundaries between the regions can be written sigma 1 dV1/d straightphi (straightphi = alpha) = sigma 2 dV2/ d straightphi (straightphi = alpha) sigma 2 dV3/d straightphi (straightphi = pi - alpha) = sigma 2 dV2/ d straightphi [straightphi = pi - alpha) From the symmetry of the problem we see that V (-straightphi) = V (straightphi) V (pi - straightphi) = -V(straightphi) And in particular V(r = 0) = 0 = V[straightphi = + pi /2] Since the potential is zero at the origin, the radial function is only r^k. The symmetry condition suggests that the angular