In your own words, explain the mechanism by which charge storing capacity is increased by the insertion of a dielectric material within the plates of a capacitor.

Short Answer

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Answer: The insertion of a dielectric material within the capacitor plates increases its charge storing capacity by reducing the net electric field and voltage between the plates, while keeping the charge the same, which results in an increase in the capacitance value. The dielectric material creates a counter electric field, causing this reduction in the net electric field and voltage.

Step by step solution

01

Understanding the setup of a capacitor

A capacitor is an electrical component that can store energy in an electric field. It consists of two conductive plates separated by a small distance or an insulating medium, such as air or a dielectric material.
02

Basic properties of a capacitor

The quantity that characterizes a capacitor's ability to store charge is called its capacitance, which is the ratio of the charge \(Q\) on one plate to the voltage difference \(V\) between the plates. In mathematical terms: \(C = \frac{Q}{V}\). The capacitance depends on the size and shape of the capacitor plates as well as the medium between them.
03

Introducing the dielectric material

A dielectric material is an insulating material that can be polarized in the presence of an electric field. When a dielectric is inserted between the capacitor plates, its molecules align themselves with the external electric field, generating a counter electric field within the dielectric.
04

Effect of dielectric on electric field

The counter electric field generated within the dielectric opposes the external electric field, reducing the net electric field between the plates. This reduces the voltage \(V\) between the plates for a given charge \(Q\), and it can be represented as: \(V_{reduced} = V_{0} \ / \ k\), where \(V_{0}\) is the initial voltage and \(k\) is the dielectric constant of the dielectric material.
05

Effect of dielectric on capacitance

Now that the voltage is reduced, while the charge remains the same, the capacitance of the capacitor, according to the formula \(C = \frac{Q}{V}\), will increase. In fact, the new capacitance with the dielectric material can be expressed as: \(C_{new} = k C_{0}\), where \(C_{0}\) is the initial capacitance without the dielectric. The dielectric constant \(k\) is always greater than 1, hence the insertion of a dielectric material always results in an increase in the capacitance of the capacitor. In summary, the insertion of a dielectric material within the capacitor plates increases the charge storing capacity of the capacitor by reducing the net electric field and voltage between the plates, while keeping the charge the same, which results in an increase in the capacitance value.

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