Aplate is positioned in the xy plane which has an infinite length in the x-direction. the y = 0 and y=l edges are held at t =0 k with the x=0 edge held at 1000 k. re watermark now a) make a labelled sketch of the problem. b) state or derive all general solutions of laplace's equation for this set-up. c) define boundary conditions for all 4 edges including a formula y conditions for all 4 edges including a formula for t(0,y) and hence [4] explain which boundary conditions rule out which general solutions. d) express the remaining solution as a series and find the necessary comm series. e) write out the solution to this problem. nd find the necessary coefficients of this [4] memow walmark now 12 an thin plate is positoned in the xy plane with corners at (0, 0), (10,0), (10, 30) and (0, 30). three edges are kept at a temperature of 0 kelvin whilst the y=0 edge is kept at 100 k. solve the laplace equation to find the temperature profile t(x, y) of the plate assuming steady state conditions. to do this, a) sketch out the problem. b) state or derive all general solutions of laplace's equation. releme c) define boundary conditions for all 4 edges including a formula for t (x,0) and hence explain which boundary conditions rule out which general solutions. d) express the remaining solution as a series and write down the fourier integral. e) solve the fourier integral in order to find the neccessary coefficients.