Medium $$1$$ has the electrical permittivity $${\varepsilon _1} = 1.5\,\,{\varepsilon _0}\,\,\,F/m$$ and occupies the region to left of $$x = 0$$ plane. Medium $$2$$ has the electrical permittivity $${\varepsilon _2} = 2.5\,\,{\varepsilon _0}\,\,\,F/m$$ and occupies the region to the right of $$x = 0$$ plane. If $${E_1}$$ in medium $$1$$ is $${E_1} = \left( {2\,{u_x} - 3\,{u_y} + 1\,{u_z}} \right)$$ volt/m, then $${E_2}$$ in medium $$2$$ is

If the electric field intensity associated with a uniform plane electromagnetic wave traveling in a perfect dielectric medium is given by

$$E\left( {z,\,t} \right) = \,10\,\cos \left( {2\pi \times {{10}^7}\,\,t - 0.1\,\,\pi z} \right)\,$$ volt/m, the velocity of the traveling wave is

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