Explanation:

The charge buildup in a capacitor is due to the displacement current density. To understand why, let's first look at the basic working principle of a capacitor.

A capacitor consists of two conducting plates separated by an insulating material called a dielectric. When a voltage is applied across the plates, an electric field is generated in the dielectric material. This electric field causes the charges (electrons or ions) in the conducting plates to redistribute, resulting in a buildup of charge on each plate.

Displacement Current Density:
Displacement current is a concept introduced by James Clerk Maxwell to explain the behavior of electric fields in changing magnetic fields. According to Maxwell's equations, a changing electric field can induce a magnetic field, and similarly, a changing magnetic field can induce an electric field. The concept of displacement current is used to explain the latter case.

Displacement current density is represented by the symbol Id and is defined as the rate of change of electric flux with respect to time. Mathematically, it is given by:

Id = ε₀ * dE/dt

where ε₀ is the permittivity of free space and dE/dt is the rate of change of the electric field.

Charge Buildup:
When a voltage is applied across the plates of a capacitor, an electric field is established between the plates. This electric field causes the displacement current to flow through the dielectric material, even though there is no physical flow of charge.

As the displacement current flows, it charges up the capacitor plates, resulting in a buildup of charge on each plate. The amount of charge stored in a capacitor is directly proportional to the voltage applied across it, and inversely proportional to its capacitance.

Conclusion:
In conclusion, the charge buildup in a capacitor is due to the displacement current density. The concept of displacement current, introduced by Maxwell, explains the behavior of electric fields in changing magnetic fields. When a voltage is applied across the plates of a capacitor, an electric field is established, causing the displacement current to flow and charge the capacitor plates.