A parallel-plate air capacitor is made from two plates 0.200...

A parallel-plate air capacitor is made from two plates 0.200 m square, spaced 0.800 $\mathrm{cm}$ apart. It is connected to a $120-\mathrm{V}$ battery. (a) What is the capacitance? (b) What is the charge on each plate? (c) What is the electric field between the plates? (d) What is the energy stored in the capacitor? (e) If the battery is disconnected and then the plates are pulled apart to a separation of $1.60 \mathrm{cm},$ what are the answers to parts (a), (b), $(c),$ and $(d) ?$

Key Concepts

Parallel-Plate Capacitors

This concept involves a device made of two conductive plates separated by an insulating material, where the capacitor’s ability to store electric charge is determined by the physical characteristics of the plates and the separation between them. It is fundamental in understanding how capacitors operate in various circuits and applications.

Capacitance Calculation

Capacitance is a measure of a capacitor’s ability to store charge per unit voltage and in a parallel-plate capacitor it is calculated using the formula C = ??A/d, where A is the area of one plate, d is the distance between the plates, and ?? is the permittivity of free space. This relationship underscores the importance of geometry and material properties in capacitor design.

Charge on a Capacitor

The charge stored on a capacitor is directly related to its capacitance and the voltage applied across it, as expressed by Q = CV. This relationship is central to many applications of capacitors in circuits, where controlling and predicting the amount of stored charge is crucial for proper circuit function.

Electric Field in a Capacitor

Between the plates of an ideal parallel-plate capacitor, the electric field is approximately uniform and is given by E = V/d, where V is the potential difference across the plates and d is the separation between them. This concept is key in understanding the behavior of the electric field in capacitive systems and its influence on charged particles.

Energy Stored in a Capacitor

A capacitor stores energy in the electric field created between its plates. The energy can be calculated by formulas such as U = ½CV², indicating that the stored energy depends on both the capacitance and the square of the voltage. This concept is important for understanding energy management and transfer in capacitive circuits.

Effects of Changing Plate Separation

Altering the distance between the plates of a capacitor affects its capacitance, which in turn influences the voltage across the plates and the energy stored within the capacitor. Depending on whether the capacitor remains connected to a battery (constant voltage) or is isolated (constant charge), the behavior of these quantities changes, demonstrating critical concepts in capacitor behavior under different physical constraints.

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