2. (Chap 11) (15pts) Two infinitely-long grounded plates, at y = 0 and y = a, are connected at x= tb by metal conducting strips. The metal strips are maintained at a constant potential Vo, as shown in Fig. 3. (a) Find the potential inside the resulting rectangular pipe from Laplace's equation, V²V=0 by using separation of variables, where the boundary conditions are V=0 when y = 0 V=0 when y = a • V = Vo when y = b V=Vo when y = -b (b) Use MATLAB to plot the potential for the first 10 modes. VO Ve VO -b 1 (Hint/Help) The independent differentials, which result from the separation of variables, are d² X(x) dr² - k²x(x) = 0 -> X(x)=Ae+ Be-k d-Y(y) dy² +k²Y(y) = 0 + = Y(y) C sin(ky) + D cos(ky).