Which one of the following field patterns represents a TEM wave traveling in the positive $$x$$ direction?

If the electric field of a plane wave is $$$\overrightarrow E \left( {z,t} \right) = \widehat x3\cos \left( {\omega t - kz + {{30}^ \circ }} \right) - \widehat y4\sin \left( {\omega t - kz + {{45}^ \circ }} \right)\left( {mV/m} \right)$$$

The polarization state of the plane wave is

For a rectangular waveguide of internal dimensions $$a\,\, \times \,\,b$$ (a > b), the cut-off frequency for the $$T{E_{11}}$$ mode is the arithmetic mean of the cut-off frequencies for $$T{E_{10}}$$ mode and $$T{E_{20}}$$ mode. If a $$ = \sqrt 5 \,cm$$, the value of b (in cm) is

Assume electronic charge q = 1.6×10^-19 C, kT/q = 25 mV and electron mobility μ_n = 1000 cm²/V-s. If the concentration gradient of electrons injected into a P-type silicon sample is 1×10²¹/cm⁴, the magnitude of electron diffusion current density (in A/cm²) is _________.