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 ________________.

An n–type silicon sample is uniformly illuminated with light which generates 10²⁰ electron hole pairs per cm³ per second. The minority carrier lifetime in the sample is 1 $$\mathrm\mu$$s.In the steady state, the hole concentration in the sample is approximately 10^x , where x is an integer. The value of x is __________________

A piece of silicon is doped uniformly with phosphorous with a doping concentration of $$10^{16}/cm^2$$. The expected value of mobility versus doping concentration for silicon assuming full dopant ionization is shown below. The charge of an electron is $$1.6\;\times\;10^{-19}\;C$$. The conductivity (in S cm^-1) of the silicon sample at 300 K is _________________.

A dc voltage of 10V is applied across an n–type silicon bar having a rectangular cross–section and a length of 1cm as shown in figure. The donor doping concentration N_D and the mobility of electrons $$\mu$$n are $$10^{16}$$ cm^-3 and 1000 cm² V^-1s^-1, respectively. The average time (in $$\mu$$s) taken by the electrons to move from one end of the bar to other end is _______________.