The electric and magnetic fields for the TE mode propagating down a rectangular waveguideare given by:nncosAmnE =|sin () ei(kzz-wt)-AmnMA•sin(et(kz-wt)cosmak,AmnsincosawB =Amnnnk,mnysincosle!(kzz-wt)k² – k?iAmnNnyCosleilkzz-wt)cos(a) Show that the electric field satisfies V. E = 0.(b) Show that applying V × E =leads to the condition:at(=) + 4) + k = k²as being equal. There(To do this, you only need to set the z-components of ▼ × E andis no need to consider the x and y components].at

This question can be solved by using rules of the electrodynamics

The electric and magnetic fields for the TE mode propagating down a rectangular waveguide are given by: mnx пл CoS nny |sin ()eilkez-we) Amn E = -Amn Mny cos -sin Amn mak, sin aw cos e!(kgz-wt) B = Amn' nak, mnx |sin COS e!(kgz-wt) k² – k; max плу cos iAmn lei(kaz-wt) Cos (a) Show that the electric field satisfies V. E = 0. (b) Show that applying 7 x E = at leads to the condition: + k = k² (To do this, you only need to set the z-components of V × E and is no need to consider the x and y components]. as being equal. There at

The electric and magnetic fields for the TE mode propagating down a rectangular waveguide are given by: mnx пл CoS nny |sin ()eilkez-we) Amn E = -Amn Mny cos -sin Amn mak, sin aw cos e!(kgz-wt) B = Amn' nak, mnx |sin COS e!(kgz-wt) k² – k; max плу cos iAmn lei(kaz-wt) Cos (a) Show that the electric field satisfies V. E = 0. (b) Show that applying 7 x E = at leads to the condition: + k = k² (To do this, you only need to set the z-components of V × E and is no need to consider the x and y components]. as being equal. There at