An air-filled rectangular waveguide has dimensions a=10.922 cm and b=5.461 cm. The waveguide is operating in the fundamental TE10 mode. The corresponding field expressions for the TE10 mode are given by; H(x, y, z) =A10 cos-xe-iz -jwun a Ey(x, y, z) = ka A10 sin-xe-jz a Hx(x,y,z) = ka A10 sin-xe-iz where; Ao is an arbitrary constant and is the propagation constant. i. Plot the electric field distribution along the cross section of the [6 marks] waveguide. ii. Plot the magnetic field distribution along the cross section of [6 marks] the waveguide. iii. If the breakdown voltage of air is 3MV/m, determine the [6 marks] maximum power that can be transmitted through the wveguide. The frequency of operation is 2 GHz. B. [15 marks] Let uo H() represent a noisy image defined in N. Consider the two minimization problems (u) = |Vu|2 + |u - uo|dx Minimize (i) within the set X := H(n) and Minimize J(u) = | Vu+ u uo|2dx (ii) within the set X= {u W (N) : ulan = 0}