1. The problem statement, all variables and given/known data Given the Z component of E inside a rectangular wave guide, Find the ratio of the maximum charge density on the plane x = 0 to the maximum charge density on the plane y = 0. Additionally, Find the ratio of the maximum surface current on the x = 0 plane to the maximum surface current on the y = 0 plane. I dont need someone to work out the problem for me, i just need help with the general approach. I can be more specific with the exact electric field given if necessary. 2. Relevant equations 3. The attempt at a solution since my z component of E is non zero, I know i must have a TM mode since rectangular wave guides do not support TEM mode waves. therefore, my z component of B = 0, and i can then go ahead and calculate the different components of my electromagnetic fields from equations derived in my book. At this point, i know what my E and B fields are inside the wave guide. My book also says we assume that wave guides are perfect conductors so that E=B=0 inside the walls and that free charges and currents will be induced onto the walls in order to maintain the boundary conditions at the inner wall that E parallel and B perpendicular must both be 0. Do i try and use these boundary conditions to find out my charge and current densities?