Relative Permittivity Assignment Help

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 

fm = 1 / 4π∈ q1 q2 / r2

Dividing (6) by (7) we get

f0 / fm = ∈/∈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 = Cm / C0

Thus Cm = 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?

Solhere Cm = 10 μF,

C0 =? K = 2

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

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