A 2.00-n F parallel-plate capacitor is charged to an...

A $2.00-n \mathrm{~F}$ parallel-plate capacitor is charged to an initial potential difference $\Delta V_{i}=100 \mathrm{~V}$ and then isolated. The dielectric material between the plates is mica $(\kappa=$ $5.00$ ). (a) How much work is required to withdraw the mica sheet? (b) What is the potential difference of the capacitor after the mica is withdrawn?

Key Concepts

Capacitors

Capacitors are electronic components that store energy in the electric field created between two conductors. Their ability to store charge is quantified by capacitance, which depends on the geometry of the conductors and the properties of the insulating material between them.

Dielectric Materials

Dielectric materials are insulators placed between the plates of a capacitor to increase its capacitance by reducing the effective electric field. The effectiveness of a dielectric is characterized by its dielectric constant (or relative permittivity), which scales the capacitance relative to that of an air-gap capacitor.

Energy Stored in a Capacitor

The energy stored in a capacitor can be expressed by formulas such as U = ½ CV² when the voltage is constant or U = Q²/(2C) when the charge is constant. This concept is crucial because variations in the capacitor’s physical properties (like the presence or absence of a dielectric) change the stored energy.

Isolated Capacitors (Constant Charge Condition)

When a capacitor is isolated from a voltage source, its charge remains constant even if its capacitance changes. Under this constant charge condition, removing or inserting a dielectric alters the potential difference and the stored energy, which is fundamental for analyzing work done during these processes.

Work in Dielectric Removal

The work required to remove a dielectric from an isolated capacitor is equal to the change in the stored energy of the capacitor. This energy difference, computed before and after the removal, represents the mechanical work needed to overcome the attractive forces between the dielectric and the capacitor plates.

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