Let's understand the concept of relative permittivity and its value for slate dielectric.

Understanding Relative Permittivity

Relative permittivity, also known as the dielectric constant (\(\varepsilon_r\)), is a measure of how an electric field affects, and is affected by, a dielectric medium. It is the ratio of the permittivity of the substance (\(\varepsilon\)) to the permittivity of free space (\(\varepsilon_0\)):

\(\varepsilon_r = \frac{\varepsilon}{\varepsilon_0}\)

It indicates how much the electric field is reduced when it passes through the dielectric material compared to when it passes through a vacuum. A higher relative permittivity means the material is more effective at reducing the electric field and storing electrical energy.

Relative Permittivity Range for Slate Dielectric

Different materials have different values of relative permittivity. These values can vary depending on the specific composition and structure of the material.

For slate, which is a fine-grained, foliated metamorphic rock, when used as a dielectric material, its typical relative permittivity falls within a specific range.

The relative permittivity of slate dielectric is commonly found to be in the range of 6 to 7.5.

This value indicates that slate can reduce an electric field by a factor of approximately 6 to 7.5 compared to a vacuum.

Considering the given options, the range 6-7.5 aligns with the typical values for the relative permittivity of slate dielectric.