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

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

A uniform plane wave traveling in air is incident on the plane boundary between air and another dielectric medium with $${\varepsilon _r} = 4$$. The reflection coefficient for the normal incidence, is

The depth of penetration of electromagnetic wave in a medium having conductivity $$\sigma $$ at a frequency of 1 KHz is 25 cm. The depth of penetration at a frequency of 4 KHz will be