Question

A space is filled up with a charge with volume density ρ = ρ₀ e^-αr ³, where ρ₀ and α are positive constants, r is the distance from the centre of this system. Find the magnitude of the electric field strength vector as a function of r. Investigate the obtained expression for the small and large values of r, i.e. at αr³ <<1 and αr³ > > 1.

Answer 1

Let us consider a spherical layer of radius r and thickness dr, having its centre coinciding with the centre of the system. Then using Gauss’ theorem for this surface,

After integration