In an air-filled rectangular waveguide, the vector electric field is given by $$\mathop E\limits^ \to = \cos \,(20\,\pi \,y)\,\exp \,\,\left[ { - j\left( {{{40\,\,\pi } \over 3}} \right)\,z\, + j\,\omega \,t} \right]\,\hat i\,\,\,V/m$$

Find the vector magnetic field and the phase velocity of the wave inside the waveguide.

A rectangular hollow metal waveguide is required to be so designed to propagate a 9375 MHz signal in its $$T{E_{10}}$$-mode that the guide-wavelength equals the cut-off wavelength. Calculate the value of 'a' (breadth or the wider dimension of the waveguide). Take b = a/2. Also, calculate the cut-off frequency of the next higher order mode.

A rectangular hollow metal waveguide of internal cross-section of $$7.366\,\,cm\,\, \times \,\,3.556\,cm$$ carries a 3 GHz signal in the $$T{E_{10}}$$-mode. Calculate the maximum power handling capability of the waveguide assuming the maximum permissible electric field inside the waveguide to be 30 kV/cm