In a source free region in vacuum, if the electrostatic potential $$\varphi\;=\;2x^2\;+y^2+cz^2$$ , the value of constant c must be ________________.

The electric field of a uniform plane electromagnetic wave is $$$\vec E = \left( {{{\overrightarrow a }_x} + j4{{\overrightarrow a }_y}} \right)\exp \left[ {j\left( {2\pi \times {{10}^7}t - 0.2z} \right)} \right]$$$

The polarization of the wave is

The electric field intensity of a plane wave propagating in a lossless non-magnetic medium is given by the following expression
$$\overrightarrow E \left( {z,t} \right) = {\widehat a_x}5\cos \left( {2\pi \times {{10}^9}t + \beta z} \right)$$ $$$ + {\widehat a_y}3\cos \left( {2\pi \times {{10}^9}t + \beta z - {\pi \over 2}} \right)$$$

The type of the polarization is

An air-filled rectangular waveguide of internal dimension $$a\,\,cm\,\, \times \,\,b\,\,cm$$ (a > b) has a cutoff frequency of 6 GHz for the dominant $$T{E_{10}}$$ mode. For the same waveguide, if the cutoff frequency of the $$T{E_{11}}$$ mode is 15 GHz, the cutoff frequency of the $$T{E_{01}}$$ mode in GHz is _____________