Consider the following model the hydrogen atom A small point

Consider the following model the hydrogen atom. A small point change of is surrounded by a uniform spherical distribution of negative charge with constant charge density rho and radius, r_0. Using the fact that hydrogen atom is neutral, find rho_0 in terms of q and r_0. Find the potential at any distance r from the center.

Solution

rho_not = charge/surface area = q/(4*pi*r₀²)

from V = Q/(4*pi*epsilon_not*r₀) valid for 0<r<r₀

V = 0 for r>r₀