Problem 32 - Arihant AIEEE Physics

Question

For the metallic conductor: (a) dielectric constant must be zero (b) dielectric constant must not be infinity (c) dielectric constant must be infinity (d) dielectric constant may be infinity

Step-by-Step Solution

Answer

For metallic conductors, the dielectric constant must be infinity (option c).

Step 1: Understanding Dielectric Constant

The dielectric constant, also known as the relative permittivity, measures a material's ability to store electrical energy in an electric field. For metallic conductors, the dielectric constant has a different behavior compared to insulators or semiconductors.

Step 2: Concept of Metallic Conductor

A metallic conductor is a material with free charge carriers (electrons) that can move easily through the substance. Conductors allow electric current to pass through them with minimal resistance.

Step 3: Dielectric Constant in Metallic Conductors

In metallic conductors, the dielectric constant is essentially infinite due to the presence of free charges that can migrate, allowing the conductor to effectively respond to an external electric field by generating large induced charges that fully oppose the field.

Key Concepts

Metallic Conductors

Metallic conductors are materials that display exceptional conductive properties. They possess free electrons, which can move throughout the material freely. This ability allows them to conduct electric current efficiently with minimal resistance.

When an electric field is applied to a metallic conductor, these free electrons move in response to that field. This movement of charge is what allows metallic conductors to carry electric current so effectively. Consequently, metallic conductors like copper or silver are widely utilized in electrical wiring and circuitry.

• Conductivity is due to free electrons.
• Metals like copper and silver are common examples.
• Conductors show little resistance to electric current.

Relative Permittivity

Relative permittivity, also referred to as the dielectric constant, quantifies a material's capacity to store electrical energy when exposed to an electric field. It is the ratio of the permittivity of a substance to the permittivity of free space, which is a constant.

Different materials have varying relative permittivity values. Non-conductors typically have a finite relative permittivity, allowing them to store electromagnetic energy moderately. However, for metallic conductors, the unique presence of free charges leads to a scenario where the relative permittivity can be considered infinite. This infinite value arises because the conductor can polarize strongly in response to an electric field, essentially canceling the field within itself.

• Dielectric constant is key for energy storage in fields.
• Infinity in metallic conductors reflects strong polarization.
• Measured as the ratio to permittivity of space.

Electric Field Response

When an electric field is applied to a material, it generally reacts in a way that depends on its properties. Metallic conductors exhibit a remarkable response due to their ability to polarize fully.

In metallic conductors, the electric field causes free electrons to shift, creating an internal field that opposes and thus neutralizes the external field. This response is almost perfect, meaning that inside a perfect conductor, the net electric field is zero due to this full counteracting response. This property is what makes such materials excellently suited for shielding electrical components from external electric disturbances.

• Conductors' response results in field cancellation inside.
• Free electrons move to counter the applied field.
• Effective in electrical shielding applications.