Introduction:
When discussing the flow of current in a circuit, it is important to differentiate between conduction current and displacement current. Conduction current refers to the movement of electric charges through a conducting medium, such as a wire, while displacement current refers to the change in electric flux through a region of space.

Explanation:
Outside the capacitor plates, we only have conduction current and no displacement current due to several reasons:

1. Capacitor Structure:
The structure of a capacitor consists of two parallel plates separated by a dielectric material. The conduction current flows through the conducting plates and the connecting wires, while the displacement current is associated with the changing electric field between the plates.

2. Flux Conservation:
The principle of flux conservation states that the total electric flux entering a closed surface must be equal to the total electric flux leaving that surface. In the case of a capacitor, the electric flux entering one plate must be equal to the electric flux leaving the other plate.

3. Electric Field Lines:
The electric field lines between the capacitor plates are perpendicular to the surface of the plates. Thus, the electric field lines do not cross the region outside the plates. As a result, there is no change in electric flux through this region, leading to zero displacement current.

4. Closed Loop Conduction Path:
The conduction current flows through a closed loop that includes the capacitor plates and the connecting wires. This closed loop ensures the continuity of the conduction current, allowing the electric charges to flow without interruption.

5. Conservation of Charge:
According to the principle of charge conservation, the total charge entering a closed surface must be equal to the total charge leaving that surface. In the case of a capacitor, the charges accumulating on the plates are balanced by an equal and opposite charge on the other plate, ensuring the conservation of charge.

Conclusion:
Due to the structure of a capacitor, the conservation of electric flux, the direction of electric field lines, the closed loop conduction path, and the conservation of charge, we only have conduction current outside the capacitor plates. The absence of displacement current in this region is a fundamental characteristic of capacitors and plays a crucial role in various electrical circuits and applications.