A rectangular metal wave guide filled with a dielectric material of relative permittivity $${\varepsilon _r} = \,4$$ has the inside dimensions $$3.0\,cm\,\, \times \,\,1.2\,cm$$. The cut-off frequency for the dominant mode is

Two identical antennas are placed in the $$\theta = \pi /2$$ plane as shown in figure. The elements have equal amplitude excitation with 180° polarity difference, operating at wavelength λ. The correct value of the magnitude of the far zone resultant electric field strength normalized with that of a single element, both computed for $$\phi = 0$$ is

n-type silicon is obtained by doping silicon with

The electron concentration in a sample of uniformly doped n-type silicon at 300^oK varies linearly from $$10^{17}/cm^3$$ at x = 0 to $$6\times10^{16}/cm^3$$ at x = 2 $$\mu m$$. Assume a situation that electrons are supplied to keep this concentration gradient constant with time.If electronic charge is $$1.6\times10^{-19}\;coulomb$$ and the diffusion constant $$D_n=3\;cm^2/s$$, the current density in the silicon, if no electric field is present is