A plane wave of wavelength $$\lambda $$ is traveling in a direction making an angle $${{{30}^ \circ }}$$ with positive $$x$$-axis and $${{{90}^ \circ }}$$ with positiv $$y$$-axis. The $$\overrightarrow E $$ field of the plane wave can be represented as ($${E_0}$$ is a constant)

A load of 50 $$\Omega $$ is connected in shunt in a 2-wire transmission line of $$Z_0$$ = 50 $$\Omega $$ as shown in the Fig. The 2-port scattering parameter matrix (S-matrix) of the shunt element is

The parallel branches of a 2-wire transmission line are terminated in 100 $$\Omega $$ and 200 $$\Omega $$ resistors as shown in the Fig. The characteristic impedance of the line is $$Z_0$$ = 50 $$\Omega $$ and each section has a length of $$\lambda /4$$. The voltage reflection coefficient $$\Gamma $$ at the input is:

If C is a closed curve enclosing a surface S, then the magnetic field intensity $$\overrightarrow H $$, the current density $$\overrightarrow J $$ and the electric flux density $$\overrightarrow D $$ are related by