A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10$$-$$4 cm, with air as the dielectric. Assume the speed of light in air to be 3 $$\times$$ 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/are ___________.
In an electrostatic field, the electric displacement density vector, $$\overrightarrow D $$, is given by
$$\overrightarrow D (x,y,z) = ({x^3}\overrightarrow i + {y^3}\overrightarrow j + x{y^2}\overrightarrow k )$$ C/m2,
where, $$\overrightarrow i $$, $$\overrightarrow j $$, $$\overrightarrow k $$ are the unit vectors along x-axis, y-axis, and z-axis, respectively. Consider a cubical region R centered at the origin with each side of length 1 m, and vertices at ($$\pm$$ 0.5 m, $$\pm$$ 0.5 m, $$\pm$$ 0.5 m). The electric charge enclosed within R is __________ C (rounded off to two decimal places).
Consider a long rectangular bar of direct bandgap p-type semiconductor. The equilibrium hole density is 1017 cm$$-$$3 and the intrinsic carrier concentration is 1010 cm$$-$$3. Electron and hole diffusion lengthss are 2 $$\mu$$m and 1 $$\mu$$m, respectively. The left side of the bar (x = 0) is uniformly illuminated with a laser having photon energy greater than the bandgap of the semiconductor. Excess electron-hole pairs are generated ONLY at x = 0 because of the laser. The steady state electron density at x = 0 is 1014 cm$$-$$3 due to laser illumination. Under these conditions and ignoring electric field, the closest approximation (among the given options) of the steady state electron density at x = 2 $$\mu$$m, is _____________.
In a non-degenerate bulk semiconductor with electron density n = 1016 cm$$-$$3, the value of EC $$-$$ EFn = 200 meV, where EC and EFn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 1010 cm$$-$$3. For n = 0.5 $$\times$$ 1016 cm$$-$$3, the closest approximation of the value of (EC $$-$$ EFn), among the given options is _________.