{ Consider the 2-dimensional Poisson equation, (82 +82)(,y) = p(,y), (8) and assume that we have a charge density which is constant inside a radius ro from the origin and zero outside, pr) = (9) or > TO with r= 7+ ya a) (3 Points) Given that the 2D Laplace operator, 82 + 6, has the following Green's function: Gr.y.3'31) - In [(x - 2) + (-y)?] , (10) write down an integral equation for the solution (r,y). (Do not carry out the integral.) b) (5 Pointa) Assuming we are far from the source, r>ro, determine an approximate (lowest-order) solution (z.y). Hint: express the integral in 2D polar coordinates and neglect any terms of order { Consider the 2-dimensional Poisson equation, (82 +82)(,y) = p(,y), (8) and assume that we have a charge density which is constant inside a radius ro from the origin and zero outside, pr) = (9) or > TO with r= 7+ ya a) (3 Points) Given that the 2D Laplace operator, 82 + 6, has the following Green's function: Gr.y.3'31) - In [(x - 2) + (-y)?] , (10) write down an integral equation for the solution (r,y). (Do not carry out the integral.) b) (5 Pointa) Assuming we are far from the source, r>ro, determine an approximate (lowest-order) solution (z.y). Hint: express the integral in 2D polar coordinates and neglect any terms of order