Question

A material has dielectric constant 2. If permittivity of free space is 8.85 × 10^-12 Fm^-1, then permittivity and relative permittivity of the dielectric respectively are, 
1. 8.85 × 10-12 Fm-1 and 1
2. 17.7 × 10-12 Fm-1 and 2
3. 8.85 × 10-12 Fm-1 and 2
4. 17.7 × 10-12 Fm-1 and 1

Answer 1

Correct Answer - Option 2 : 17.7 × 10-12 Fm-1 and 2

CONCEPT:

Dielectric constant

• Dielectric is a material that has poor electrical conductivity but has the capability to retain or store electric charge in it.
  • The dielectric constant of a given material is defined as the ratio of the permittivity of the material (ϵ) to the permittivity of the free space (ϵ0).
  • This ratio is also known as the relative permittivity of the dielectric.
• The dielectric constant, 

\(⇒ K = \frac{ϵ}{ϵ_0}\)

• The relative permittivity of a dielectric, 

\(⇒ ε _r = \frac{ϵ}{ϵ_0}\)

• The dielectric constant K of a material is defined as

\(⇒ K=\frac {\sigma}{\sigma - \sigma_p}\)

where σ is the induced charge density in the case of a conductor and σp is the induced charge density in the case of a dielectric in the same external electric field.

​EXPLANATION:

Given, the dielectric constant K = 2

• The dielectric constant of a dielectric, 

\(⇒ K = \frac{ϵ}{ϵ_0} =2\)

⇒ ε = 2 × ε₀ = 2 × 8.85 × 10^-12 = 17.7 × 10^-12 Fm^-1

• The relative permittivity of a dielectric, 

\(⇒ K = \frac{ϵ}{ϵ_0} = ε _r = 2\)

Therefore option 2 is correct.