Electrostatics - Relative Permittivity

Relative Permittivity

According to coulomb’s law, the force of interaction between two charges q1 and q2 separated by a distance r in vacuum is

f₀ = 1 /4π∈₀ q₁ q₂ / r²

Where ∈0 is absolute electrical permittivity of free space.

If the same two charges are held the same distance apart in a material medium then the force of interaction between them is 

f_m = 1 / 4π∈ q₁ q₂ / r²

Dividing (6) by (7) we get

f₀ / f_m = ∈/∈₀ = ∈r or k

Where ∈r is relative electrical permittivity or dielectric constant (k) of the material medium.

From we may also define dielectric constant of a medium as the ratio of the electrostatic force of interaction between two given point charges held certain distance apart in vacuum/air tot eh force of interaction between the same two charges held the same distance a part in the material medium. 

Faraday observed that when an insulating material is fully occupying the space between the charged plates of a capacitor, its capacitance increases. The factor by which capacitance is multiplies depends on the nature of the dielectric introduced, and is called relative permittivity (∈) or dielectric constant (k) of the material, we may write.

∈r or  k = capacitance of a capacitor with dielectric in-between the plates / capacitance of the same capacitor with vacuum / air in between the plates 

∈r or K = C_m / C₀

Thus C_m = KC₀ = ∈r ∈₀A / d = ∈A / d

The values of ∈r or K for common dielectric materials are given in table

Table (d) dielectric constant for some common dielectrics 

Material	ε r or K	Material	ε r or K
Vacuum	1.0000	paraffined paper	2.1-2.3
Air (I atm)	1.0548	porcelain	6 – 7
Air (100 atm)	1.0548	germanium	16
Hydrogen	1.00026	glass	3 – 4
Turpentine	2.23	alcohol	25
Teflon	2.1	transformer oil	2.24
Amber	2. 8	water	81
Mica	6 – 7

The capacity of a capacitor becomes 10 u F when air between the plates is replaced by a dielectric slab of K = 2 what is the capacity of the condenser with air in between the plates?

Sol: here C_m = 10 μF,

C₀ =? K = 2

As k = C_m / C₀ ∴ C₀ = C_m / K = 10 / 2 = 5 u F

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