A spherical conducting shell has two concentric surfaces, an inner one with radius a, and an outer one with radius 17. The conductor has a uniform conductivity 0'. Its electric and magnetic susceptibilities can be neglected (i.e. no polarization and magnetization). Outside the conducting shell is free space. Initially at t = 0, there is an amount of charge q uniformly distributed on the inner surface. We would like to nd out the system's behavior at t > 0. [Note: This is not a quasi-stationary process apply the full Maxwell's equations] Figure 2: A spherical conducting shell. Show that the volumetric charge density at a 0. Also show that the total amount of charge on the inner surface Cin (t) at r = a decreases following an exponential time dependence: Q(t) = qet/T. (1) Find out the characteristic time constant 7 in terms of the parameters of the problem. [Hint: Use Maxwell's equation and Ohm's law. Also consider applying Gauss's law to relate electric field and charge at any given time.]Find out the current density inside the conductor fort > 0. Then calculate the total amount of Joule heat production as the conductor settles down to electrostatic equilibrium at I ) 00. If the shell is a perfect conductor (corresponding to the limit of an infinitely large conductivity o -> co), is there any energy dissipation via Joule heating as the system settles down to electrostatic equilibrium?The energy density stored in the electric field is up = (1/2) &o E. Calculate the total energy stored in the field, both at the initial time t = 0, and at t -> co. Does the amount of change in the field energy equal to the Joule heating you find out in Part (3)