The answer to the question is option 'B' - Displacement current.

Explanation:

1. Introduction to Capacitors:
A capacitor is an electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by an insulating material called the dielectric. When a voltage is applied across the plates, the capacitor charges up, storing electrical energy.

2. Charge Build-up in a Capacitor:
The charge build-up in a capacitor occurs when electrons flow from one plate to the other, resulting in a potential difference between the plates. This charge build-up leads to the accumulation of positive and negative charges on the respective plates.

3. Conduction Current:
Conduction current refers to the flow of electric charges through a conductor, such as a wire. In the case of a capacitor, once the voltage is applied, an initial conduction current flows from the source through the capacitor plates, charging them up. However, this conduction current is not responsible for the actual charge build-up in the capacitor.

4. Displacement Current:
Displacement current, proposed by James Clerk Maxwell, is a concept that describes the flow of electric displacement field through a dielectric material. It is an important term in Maxwell's equations and is directly related to the time-varying electric field.

5. Role of Displacement Current in a Capacitor:
When a voltage is applied across a capacitor, an electric field is established between the plates. This varying electric field induces a displacement current in the dielectric material between the plates. This displacement current flows through the dielectric, contributing to the charge build-up in the capacitor.

6. Relationship between Displacement Current and Charge Build-up:
According to Maxwell's equations, the total current flowing through any closed surface is the sum of the conduction current and the displacement current. In the case of a charging capacitor, the displacement current is responsible for the change in electric flux through the dielectric, leading to the charge build-up on the plates.

Conclusion:
In conclusion, the charge build-up in a capacitor is primarily due to the displacement current. While an initial conduction current flows during the charging process, it is the displacement current induced by the varying electric field that contributes to the actual charge accumulation on the capacitor plates.