Question

The refractive index and the permeability of a medium are respectively 1.5 and 5 x 10-7 hm-1 . The relative permittivity of the medium is nearly:-

Answer 1

Hii dear,

# Answer- ϵr = 2.51

# Explaination-

Speed of light through medium

v = c/n

v = 3×10^8 / 1.5

v = 2×10^8 m/s

Velocity of light in medium,

c=1/√(ϵμ)

ϵμ = c^2

ϵ = 1/μc^2

ϵ = 1/[(5×10^-7)(3×10^8)^2]

ϵ = 2.22×10^-11 F/m

Relative permittivity =

ϵr = ϵ/ϵ0

ϵr = (2.22×10^-11)/(8.85×10^–12)

ϵr = 2.51

Relative permittivity of medium is 2.51.

Answer 2

Speed of light through medium

v = c/n

v = 3×10^8 / 1.5

v = 2×10^8 m/s

Velocity of light in medium,

c=1/√(ϵμ)

ϵμ = c^2

Thus

ϵ = 1/μc^2

ϵ = 1/[(5×10^-7)(3×10^8)^2]

ϵ = 2.22×10^-11 F/m

Now Relative permittivity is

ϵr = ϵ/ϵ0

ϵr = (2.22×10^-11)/(8.85×10^–12)

ϵr = 2.51

Thus relative permittivity of the medium is nearly 2.5.