Question : What is the relation between dielectric constant and electric suseptibillity ?
OR
Establish a relation between dielectric polarisation, electric suceptibility and dielectric constnat.
Doubt by Girisha
Solution :
When a dielectric is placed in an external electric field E, its molecules become polarised.
The polarization P (dipole moment per unit volume) is directly proportional to the applied electric field.
P = ε₀χₑE — (1)
[Note that in when CGS units are choosen the the formula was P = χₑE but when SI units are choose then the formula will be P = ε₀χₑE]
where,
P = Polarisation
ε₀ = Permittivity of free space
χₑ = Electric susceptibility
E = Applied electric field
Also, the dielectric constant K (or relative permittivity εᵣ) is related to electric susceptibility by
K = εᵣ = 1 + χₑ
or
χₑ = K − 1
Substituting χₑ = K − 1 in eq. (1)
P = ε₀(K − 1)E
Hence, the required relations are:
P = ε₀χₑE
K = 1 + χₑ
P = ε₀(K − 1)E
Therefore, dielectric polarisation, electric susceptibility, and dielectric constant are related by
P = ε₀χₑE = ε₀(K − 1)E
This is the required relation.
