Question

Relative permittivity and permeability of a material are \[{\varepsilon _r}\] and \[{\mu _r}\], respectively. Which of the following values of these quantities are allowed for a diamagnetic material?
A. \[{\varepsilon _r} = 1.5,\;{\mu _r} = 1.5\]
B. \[{\varepsilon _r} = 0.5,\;{\mu _r} = 1.5\]
C. \[{\varepsilon _r} = 1.5,\;{\mu _r} = 0.5\]
D. \[{\varepsilon _r} = 0.5,\;{\mu _r} = 0.5\]

Answer 1

Hint: A material's relative permittivity, or dielectric constant (\[{\varepsilon _r}\]), is its (absolute) permittivity expressed as a ratio to vacuum permittivity. Relative permeability, denoted by the symbol (\[{\mu _r}\]), is the ratio of a given medium's permeability to free space permeability.

Complete step by step answer:
In physics, a basic rule of thumb is used to determine whether a particle is paramagnetic or diamagnetic (atom, ion, or molecule). The material consisting of this particle is diamagnetic if all electrons in the particle are paired; if it has unpaired electrons, then the material is paramagnetic.

The dielectric constant often referred to as relative permittivity (\[{\varepsilon _r}\]), shows how quickly a substance can be polarized by applying an electric field on an insulator. Relative permittivity is the ratio of a substance's permittivity to the allowability of space or vacuum.
Relative permittivity can be expressed as:
\[{\varepsilon _r} = \dfrac{\varepsilon }{{{\varepsilon _o}}}\]
Here, \[{\varepsilon _r}\]=relative permittivity - of dielectric constant
\[\varepsilon \]=permittivity of substance
\[{\varepsilon _o}\]=permittivity of vacuum or free space
For any material, \[{\varepsilon _r} > 1\]
The ratio of the permeability of a given medium to the permeability of free space \[{\mu _o}\] is the relative permeability denoted by the symbol \[{\mu _r}\].
Relative permeability can be expressed as:
\[{\mu _r} = \dfrac{\mu }{{{\mu _o}}}\]
Here,\[{\mu _r}\]= relative permeability
\[\mu \]= permeability of the given medium
\[{\mu _o}\]=permeability of free space
For diamagnetic material, \[0 < \;{\mu _r}\; < 1\]
Hence, for a diamagnetic material \[{\varepsilon _r} > 1\] and \[0 < \;{\mu _r}\; < 1\].

So, the correct answer is “Option C”.

Note:
In this question we need to understand the relationship of relative permittivity and relative permeability for a diamagnetic material. Different materials execute different properties.In this question we need to understand the relationship of relative permittivity and relative permeability for a diamagnetic material. Different materials execute different properties.