(Solved): In addition to each part, please explain and show graphs, as described in the question. Charge Q has ...

Charge $\mathrm{Q}$ has been placed throughout the volume of a conducting sphere of radius a. The material of the sphere is not a perfect conductor but has finite conductivity equal to $\sigma =-10^{-3}$ $\mathrm{S}/\mathrm{m}$ and has the same permittivity as air. The surrounding medium is air. Recall ${\epsilon }_0=8.85\times 10^{12}$ $\mathrm{F}/\mathrm{m}$. a) How much time will it take for this conducting sphere to dissipate the volume charge and move all of it to the surface? Give a specific value and don't forget units. b) After enough time has passed that the conductor has dissipated volume charge and all the charge is on the surface now, calculate the electric flux density $D$ and the electric field intensity E everywhere in space. Calculate and graph $D(R)$ vs $R$ and $E(R)$ vs R. Clearly denote the values of $D(a)$ and $E(a)$. Remember, $D$ and $E$ will have a jump at points where there is a sheet of charge. c) A thick dielectric layer is added to the system (e.g., in addition to the charged sphere from before). The dielectric layer extends from $R=a$ to $R=b$ and has relative permittivity of ${\epsilon }_r=2$. Calculate and graph $D(R)$ vs $R,E(R)$ vs $R$, and $P(R)$ VS R.