Parallel plate capacitor with a sheet of My lar (κ=3.1) filling the space between the plates is

step 1 In this question, we have a parallel plate capacitor with dielectric inside. Okay, the dielectri

Parallel plate capacitor with a sheet of My lar (κ=3.1)...

Parallel plate capacitor with a sheet of $\mathrm{My}$ lar $(\kappa=3.1)$ filling the space between the plates is charged to a potential difference of $120 \mathrm{~V}$ and is then disconnected. a) How much work is required to completely remove the sheet of Mylar from the space between the two plates? b) What is the potential difference between the plates of the capacitor once the Mylar is completely removed?

Parallel plate capacitor with a sheet of $\mathrm{My}$ lar $(\kappa=3.1)$ filling the space between the plates is charged to a potential difference of $120 \mathrm{~V}$ and is then disconnected.
a) How much work is required to completely remove the sheet of Mylar from the space between the two plates?
b) What is the potential difference between the plates of the capacitor once the Mylar is completely removed?

Key Concepts

Parallel Plate Capacitor

A parallel plate capacitor consists of two conductive plates separated by an insulating material (or vacuum), and its capacitance is determined by the area of the plates, the separation distance between them, and the medium (or dielectric) between the plates. When a dielectric material is introduced, the capacitance increases proportionally to the dielectric constant, making it a central element in determining the capacitor’s ability to store charge.

Dielectric Constant

The dielectric constant (or relative permittivity) is a dimensionless measure of how much a material can increase the capacitance of a capacitor compared to a vacuum. It quantifies the material’s ability to reduce the electric field within the capacitor, thereby allowing it to store more charge at a given voltage. A higher dielectric constant means a greater effect on the capacitance.

Energy Stored in a Capacitor

The energy stored in a capacitor is given by the expressions U = ½CV² or U = Q²/(2C), where C is the capacitance, V is the potential difference, and Q is the charge. This stored energy is a crucial concept when considering processes that change the capacitor’s configuration (such as inserting or removing a dielectric) because such changes alter the capacitance and consequently the stored energy, assuming either constant voltage or constant charge conditions.

Conservation of Charge

When a capacitor is disconnected from any external circuit or voltage source, the charge on its plates remains constant. This conservation of charge is critical when analyzing processes like the removal of a dielectric, because although the capacitance changes, the constant charge condition forces a change in the potential difference across the plates to maintain the relationship Q = CV.

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