The charge density of an electrostatic field is given by the divergence of the electric displacement field (D). Let's understand this concept in detail.

- **Electric Displacement Field (D):** The electric displacement field, denoted by D, represents the total electric flux per unit area perpendicular to the direction of the flux. It is defined as the sum of the free charge density (ρf) and the polarization charge density (ρp) within a given region. Mathematically, it is expressed as D = ε0E + P, where ε0 is the permittivity of free space and E is the electric field.

- **Divergence of D:** The divergence of a vector field measures how much the field spreads or diverges from a particular point. In the context of the electric displacement field, the divergence of D represents the net outward flux of D per unit volume from a given point. Mathematically, it is expressed as ∇ · D, where ∇ is the del operator.

- **Charge Density:** Charge density, denoted by ρ, represents the amount of charge present per unit volume. In the context of an electrostatic field, the charge density is related to the electric displacement field by the equation ∇ · D = ρ, where ∇ · D represents the divergence of D.

- **Explanation of the Correct Answer:** The correct answer is option 'D' - Divergence of D. This means that the charge density of an electrostatic field is given by the divergence of the electric displacement field (D). The divergence of D represents the net outward flux of D per unit volume, which is directly related to the charge density. Therefore, by calculating the divergence of D, we can determine the charge density in a given region.

In summary, the charge density of an electrostatic field is given by the divergence of the electric displacement field (D). This relationship allows us to determine the charge distribution within a region based on the behavior of the electric displacement field.