1. The problem statement, all variables and given/known data In an infinite flat layer of thickness 2d, volume charge density is given according to the law: ρ=(ρ°)(x)/d and (-d≤x≤d). Here, x is the axis perpendicular to the plane. In the layer, there is a thin channel in which a point dipole of mass m and dipole moment p is placed. Calculate the time period of small oscillations of the dipole. 2. Relevant equations Differential form of electric field: div E = 4πρ and div E = ∂Ex/∂x + ∂Ey/∂y + ∂Ez/∂z 3. The attempt at a solution "Attempt to the solution has been made in CGS system" div E = 4πρ ∂Ex/∂x + ∂Ey/∂y + ∂Ez/∂z = 4πρ ∂Ey/∂y and ∂Ez/∂z will be zero. Therefore, ∂Ex/∂x = 4πρ =(4πρ°x)/d Ex(x) = (4πρ°)/d ∫x dx = [(4πρ°)/d]*[x2]/2 = (2πρ°x2)/d + C How will we find the constant C? What exactly will be the electric field at point d from the midpoint of the layer? Will it be 2πρ°(2d) = 4πρ°d? I am confused how to proceed from here.