Question

Dimensional formula of Dielectric constant is?

Answer 1

The dielectric constant is the ratio of the permittivity of a substance to the permittivity of free space. It is an expression of the extent to which a material concentrates electric flux, and is the electrical equivalent of relative magnetic permeability.

Answer 2

Answer:

The dimensional constant for the dielectric constant is  

$\bold{\text {Dielectric constant}=\left[I^{2} T^{4} M^{-1} L^{-3}\right]}$

Solution:

The unit of dielectric constant is Farad per metre. Farad is a derived quantity which means Farad is equal to coloumb/volt. Now the unit of dielectric constant became Couloumb per volt metre. But the volt is also a derived quantity which is equal to Joule/coulomb. Now the unit of dielectric constant is modified as $\bold{{Coulomb}^{2}\ per\ Joule\ metre}$. The joule is again a derived quantity which is equal to $\bold{\mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2}}$ and coulomb is also a derived unit which is equal to 1 A.s. So the final unit of dielectric constant is $\bold{\mathrm{A}^{2} \mathrm{s}^{2} \text { per } \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2} \mathrm{m}}$.

Mathematically, the unit of dielectric constant can be derived as

$\bold{\text { Dielectric constant k } =\frac{F}{m}}$

This is the unit of dielectric constant. This can be simplified by substituting the fundamental units in place of derived units. First replace the derived unit F to its respective fundamental unit as  

$\bold{\text { Dielectric constant k }=\frac{C / V}{m}=\frac{C}{V \cdot m}}$

We know that  

$1 C=1 A . s$

And

$1 V=1 \frac{J}{C}=\frac{1 J}{A . s}$

Thus the units of dielectric constant will be modified as  

$\text { Dielectric constant k }=\frac{A \cdot s}{\left(\frac{J}{A . s}\right) \cdot m}=\frac{(A . s)^{2}}{J \cdot m}$

Again, Joule is a derived unit which can be simplified as  

$1 J=1 \mathrm{kg} \cdot \mathrm{m}^{2} \mathrm{s}^{-2}$

Hence, the unit of dielectric constant is again modified as  

$\bold{\text { Dielectric constant k }=\frac{(A . s)^{2}}{k g \cdot m^{2} \cdot s^{-2} m}=\frac{A^{2} s^{4}}{k g m^{3}}}$

The dimensional constants for the above scientific factors are  

A = I, s = T, kg = M and m = L

Thus the dimensional constant for the dielectric constant is  

$\text {Dielectric constant}=\left[I^{2} T^{4} M^{-1} L^{-3}\right]$.