Before knowing about the dimensions of the dielectric constant, let us know about what actually the term is related to.
Dielectric constant is a quantity measuring a substance’s ability to store electrical energy in an electric field. It is also known as relative permittivity or specific capacity and it is a property of an electrical insulating material which is a dielectric. It is equal to the ratio of the capacitance of a capacitor (filled with a given material) to the capacitance of an identical capacitor in a vacuum without the dielectric material. The dielectric constant is a number with no dimensions. At room temperature, the dielectric constant for air is 1.00059, for paraffin is 2.25, for water is 78.2 and for barium titanatta is 2,000. These values exist when the electric field is applied perpendicular to the crystal’s principal axis. For liquids and solids, dielectric constant can be calculated by comparing the value of capacitance when the dielectric is in place to its value and when the capacitor is filled with air.
Dielectric Constant Formula
Dielectric constant can be mathematically expressed as:
κ is the dielectric constant
𝜺 is the permittivity of the substance
ε₀ is the permittivity of the free space
Dielectric Constant Units
Being the ratio of two like entities, it is a unitless, dimensionless quantity.
Symbol of Dielectric Constant Symbol
Also called the relative permittivity of a dielectric substance, dielectric Constant is expressed using Greek letter known as kappa ‘κ’.
Theory Related to Dielectric Constant
When the dielectric constant increases, the electric flux density increases, and the condition is such that all other factors should remain unchanged. This enables objects, such as sets of metal plates of a given size, to hold their electric charge for long periods of time, and/or also to hold large quantities of charge. Materials with high dielectric constants are applicable in the manufacture of high-value capacitors.
Dimensional Formula of Dielectric Constant
The dimension of dielectric constant is given by,
[Mº Lº Iº Tº]
M denotes Mass
L denotes Length
T denotes Time
Dielectric constant (K) = Permittivity of the substance (ε) × [permittivity of free space (ε₀)]⁻¹
As we know,, Force = [4πε]⁻¹ × [Electric Charge]² × [Distance]⁻²
Therefore, Permittivity of substance = permittivity of free space = [Charge²] × [Force]⁻¹ × [Distance]⁻² . . . . . (i)
The Dimensional Formula of:
Charge = [I¹ T¹] . . . (ii)
Distance = [Mº L¹ Tº] . . . . . (iii)
Force = [M¹ L¹ T⁻²] . . . . . (iv)
On substituting equation (ii), (iii) and (iv) in equation (i) we get,
Permittivity (ε) or (ε₀) = [Charge]² × [Force]⁻¹ × [Distance]⁻²
Or, ε = ε₀ = [I¹ T¹]² × [M¹ L¹ T⁻²]⁻¹ × [L1]⁻² = [M¹L⁻³ I² T⁴]
Therefore, the dimensions of permittivity of a substance or free space = [M¹L⁻³ I² T⁴]
Since, Dielectric constant (K) = ε × [ε₀]⁻¹
Therefore, the dimensional formula of dielectric constant is represented as [Mº Lº Iº Tº] = Dimensionless Quantity.