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A capacitor is a device that stores electrical energy in an electric field. Capacitors are essential in many electronic circuits, serving as components that can hold and release charge efficiently. A standard parallel-plate capacitor consists of two conductive plates placed parallel to each other, separated by a small distance.
The ability of a capacitor to store charge is quantified by its capacitance, which is measured in farads (F). For a parallel-plate capacitor, the capacitance is determined by the area of the plates, the distance between them, and the permittivity of the material between the plates. The formula for capacitance is:

• \[ C = \varepsilon_0 \frac{A}{d} \]
Where \(C\) is the capacitance, \(\varepsilon_0\) is the permittivity of free space, \(A\) is the area of one plate, and \(d\) is the distance between the plates.
When a voltage is applied across the plates, an electric field is created between them, causing electrons to accumulate on one plate while the other plate loses electrons, thus creating a charge separation. This action transforms the capacitor into a temporary energy storage device, which can release the stored energy when required.

Current refers to the flow of electric charge, typically measured in amperes (A). In the context of a capacitor, the current entering or leaving a capacitor relates to how quickly the charge on the capacitor changes.
When current flows into a capacitor, it causes an increase in the charge stored on the capacitor's plates. The relationship between current \(I\) and the rate of charge change \(\frac{dQ}{dt}\) on the capacitor can be expressed by:

• \[ I = \frac{dQ}{dt} \]

This formula indicates that the current is the rate at which a charge accumulates on or leaves the plates of the capacitor. In circuits with capacitors, current will initially be high when the plate charges are neutral and decreases as the capacitor becomes fully charged.
In our exercise, a current of 2.8 A flows into the capacitor, steadily altering the charge and thus changing the electric field between the capacitor's plates.

The rate of change in the context of a capacitor's electric field involves understanding how the electric field evolves as charges are added or removed.
The electric field \(E\) in a parallel-plate capacitor is directly tied to the charge density \(\sigma\) on the plates, given by:

• \[ E = \frac{\sigma}{\varepsilon_0} \]

Here, \(\varepsilon_0\) is the permittivity of free space. As the current flows and charge builds on the capacitor plates, the charge density changes, thereby altering the electric field.
To find the rate of change of this electric field \(\frac{dE}{dt}\), we utilize:

• \[ \frac{dE}{dt} = \frac{1}{\varepsilon_0} \frac{d\sigma}{dt} \]

This calculation involves the current affecting the charge per unit area. In our specific problem, knowing the current and dimensions of the plates, we compute the changing electric field rate by first determining the change in charge density over time, and then calculating how quickly the electric field shifts. This process reveals how dynamic and temporally sensitive electric fields are within capacitors.