A conducting shell of radius R is cut in half. The two hemispherical pieces are electrically separated from each other but left close together, so that the distance separating the two halves can be neglected. The upper half is maintained at a constant potential V-Vo, and the lower half is grounded (V0).

a) Determine the boundary condition at r R as a function of θ and expand it in a series of Legendre polynomials, retaining the terms up to l = 3 only.
b) Calculate the electrostatic potential V at all points outside of the surface of the conductors. Neglect terms falling faster than 1/r

Asquare 1m x 1m plate is shown below. all four of its edges are kept at 0 co. at t=0the temperature distribution is given by: y xtsins n75)=.a) using separation of variables determine the temperature distribution t(x, y,t)along the plate at any time t. b) discretize the heat conduction equation +=22222 txtusing a second-order centered difference scheme for the two second derivatives and a first-order forward euler scheme for the first derivative. using von neumann stability analysis, determine the stability criterion for the proposed discretization scheme in terms of , hand t. solve for the maximum allowable time step tmax