Capacitor

Before a circuit is connected: No current flows through the wire conductors. In equilibrium state, charges from battery move to the ends of wire conductors to prevent current from flowing. When plates are added to the ends of wire conductors, more charges move to the end plates of the wire conductors in order to prevent current from flowing. The two plates structure with large parallel surface area is called a capacitor. And the circuit symbol is

Capacitor Charging

When a empty capacitor is connected in series with a battery and a light bulb. At the initial state, electron current flows into and out of capacitor respectively, but not through the capacitor after the two wire connectors are connected to the battery. Since electron current flows through the electric bulb more freely, the electric bulb is lighted to maximum initial brightness. At the transition state, charges start to build up on capacitor. Less electron current flows through the electric bulb, the electric bulb is lighted to medium brightness. At the final state, charges built up on capacitor stops electron current from flowing finally. Fringe field of the capacitor rises until the electric field in the wire equals to zero, i.e. in equilibrium stat. No electron current flows through the electric bulb, the electric bulb is not glowing.

Capacitor Discharging

When a fully charged capacitor is connected in series with a light bulb. At the initial state, electron current flows iout of and into capacitor respectively, but not through the capacitor after the two wire connectors are connected to the light bulb. Since electron current flows through the electric bulb more freely, the electric bulb is lighted to maximum initial brightness. At the transition state, charges start to discharge from capacitor. Less electron current flows through the electric bulb, the electric bulb is lighted to medium brightness. At the final state, charges built up on capacitor is exhausted and electron current flowing capacitor stop finally. No electron current flows through the electric bulb, the electric bulb is not glowing.
Since the charged capacitor is charged under an external electric field, like charges are packed more closely. Therefore, although opposite charges attract, but the like charges are repelling more. Besides the fringe field of plates is not zero.

Capacitance

Capacitance is the ability of holding electric charge in the capacitor with respect to the corresponding change in the electric potential being applied on. 𝑄=𝐶∆𝑉 Electric field in a capacitor:𝐸=𝑄/𝐴𝜀₀, And ∆𝑉=−𝑓∫𝑖𝐸∙𝑑𝑙→|∆𝑉|=𝐸𝑠→|∆𝑉|=𝑄/𝐴𝜀0𝑠→𝑄=𝜀0𝐴𝑠|∆𝑉| Therefore, capacitance of a parallel-plate capacitor: 𝐶=𝜀0𝐴𝑠

Fringe Field of Edge

𝐸fringe=𝑄/𝐴𝜀0(𝑠𝐴)

Source and Reference

https://www.youtube.com/watch?v=DlXB4XFJtos&list=PLZ6kagz8q0bvxaUKCe2RRvU_h7wtNNxxi&index=16