With the reduction in actual permittivity, the relative permittivity ______.

Explanation:

Permittivity and Relative Permittivity

Definition: Permittivity is a measure of how much electric field is 'permitted' to pass through a material. It quantifies the ability of a material to store electrical energy in an electric field. The absolute permittivity (ε) of a material is the product of the relative permittivity (εr) and the permittivity of free space (ε0), where ε0 is a constant value approximately equal to 8.854 × 10^-12 F/m (farads per meter).

Relative permittivity, also known as the dielectric constant, is a dimensionless quantity that represents the ratio of the permittivity of a material to the permittivity of free space. It indicates how much better the material is at storing electrical energy compared to a vacuum. Mathematically, it is expressed as:

εr = ε / ε0

Working Principle: When an electric field is applied to a material, the material's molecules polarize, aligning themselves with the field. This polarization reduces the overall field within the material, allowing it to store more energy. The relative permittivity reflects the extent of this polarization effect. A higher relative permittivity means the material can store more electrical energy, while a lower relative permittivity means it stores less.

Correct Option Analysis:

The correct option is:

Option 2: reduces

When the actual permittivity (ε) of a material decreases, the relative permittivity (εr) also reduces. This relationship can be understood by revisiting the formula for relative permittivity:

εr = ε / ε0

If the absolute permittivity (ε) decreases while the permittivity of free space (ε0) remains constant, the ratio εr will decrease. This means the material's ability to store electrical energy compared to a vacuum diminishes, leading to a reduction in the relative permittivity.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: increases

This option is incorrect because a reduction in actual permittivity would not lead to an increase in relative permittivity. Since relative permittivity is directly proportional to the actual permittivity, a decrease in one leads to a decrease in the other.

Option 3: becomes zero

This option is incorrect because while a reduction in actual permittivity will lower the relative permittivity, it cannot become zero unless the actual permittivity itself becomes zero. Since actual permittivity is a positive value for all materials, relative permittivity will also remain positive and will not reach zero.

Option 4: remains the same

This option is incorrect because relative permittivity is a function of actual permittivity. If actual permittivity changes, relative permittivity will also change. Therefore, it cannot remain the same if actual permittivity is reduced.

Conclusion:

Understanding the relationship between actual permittivity and relative permittivity is crucial for analyzing the dielectric properties of materials. As explained, relative permittivity reduces when actual permittivity decreases because of their direct proportionality. This fundamental concept is essential in various fields of electrical engineering and material science, where the dielectric properties of materials play a significant role in the design and application of electronic components and systems.