The longitudinal component of the magnetic field inside an air – filled rectangular wave guide made of a perfect electric conductor is given by the following expression\({{\rm{H}}_{\rm{z}}}\left( {{\rm{x}},{\rm{y}},{\rm{z}},{\rm{t}}} \right) = 0.1\cos \left( {25{\rm{\pi x}}} \right)\cos \left( {30.3{\rm{\pi y}}} \right)\cos \left( {12{\rm{x}} \times {{10}^9}{\rm{t}} - {\rm{\beta z}}} \right)\left( {\frac{{\rm{A}}}{{\rm{m}}}} \right)\)The cross – sectional dimensions if the wave guide are given as \({\rm{a}} = 0.08{\rm{m}}\) and \({\rm{b}} = 0.033{\rm{m}}\). The mode of propagation inside the waveguide is

The longitudinal component of the magnetic field inside an air – fil

1.	The longitudinal component of the magnetic field inside an air – filled rectangular wave guide made of a perfect electric conductor is given by the following expression\({{\rm{H}}_{\rm{z}}}\left( {{\rm{x}},{\rm{y}},{\rm{z}},{\rm{t}}} \right) = 0.1\cos \left( {25{\rm{\pi x}}} \right)\cos \left( {30.3{\rm{\pi y}}} \right)\cos \left( {12{\rm{x}} \times {{10}^9}{\rm{t}} - {\rm{\beta z}}} \right)\left( {\frac{{\rm{A}}}{{\rm{m}}}} \right)\)The cross – sectional dimensions if the wave guide are given as \({\rm{a}} = 0.08{\rm{m}}\) and \({\rm{b}} = 0.033{\rm{m}}\). The mode of propagation inside the waveguide is
A.	\({\rm{T}}{{\rm{M}}_{12}}\)
B.	\({\rm{T}}{{\rm{M}}_{21}}\)
C.	\({\rm{T}}{{\rm{E}}_{21}}\)
D.	\({\rm{T}}{{\rm{E}}_{12}}\)
Answer» D. \({\rm{T}}{{\rm{E}}_{12}}\)