Okay, so I know that a capacitor is charged by the battery providing a potential difference which forces positive charge to flow from one capacitor plate to the other (Conventional Flow). This flow of charges takes place until the steady state is achieved.
1)Why do we calculate energy stored in the capacitor by assuming that a small charge $\text dq$ is displaced from one plate to the other ?
2)Does the charge actually flow through air (No dielectric)
3) Let us say that a charge of $+q$ and $-q$ has appeared on the capacitor plates and the steady state is not yet achieved. We say that a charge $\text dq$ will flow from the low potential plate to the negative terminal of the battery. The battery increase its potential by $V*\text dq$ ($V$ is the EMF) and sends it to the high potential plate. Is it absolutely necessary that THIS charge travel from the the negative plate to the positive one. I have been taught that a wire has a large number of free charge carriers (positive charge in case of conventional flow). Can t the $\text dq$ charge originate from the wire itself . If this is true then then shouldn’t the work required to move this charge to the the positive plate change since now it has NOT traveled through a potential difference of $q/C$ ($C$ is the capacitance of the capacitor).