Solveeit Logo
Login

Question

Question: The dimensional formula of dielectric strength A. \({M^1}{L^1}{T^2}{Q^{ - 1}}\) B. \({M^1}{L^2}{...

The dimensional formula of dielectric strength
A. M1L1T2Q−1{M^1}{L^1}{T^2}{Q^{ - 1}}
B. M1L2T−2Q−1{M^1}{L^2}{T^{ - 2}}{Q^{ - 1}}
C. M−1L−1T2Q1{M^{ - 1}}{L^{ - 1}}{T^2}{Q^1}
D. M−1L−1T2Q2{M^{ - 1}}{L^{ - 1}}{T^2}{Q^2}

Explanation

Solution

Before going through the question we should first know about dimension. The smallest number of coordinates required to specify a point within a mathematical space (or object) is known as its dimension in physics.

Complete step by step answer:
The term dielectric strength has the following definitions in physics:
-The maximum electric field that a pure electrically insulating material can withstand under ideal conditions without electrical breakdown and being electrically conductive (i.e. without failure of its insulating properties).

-The minimum applied electric field (i.e. the applied voltage divided by electrode separation distance) that causes breakdown for a particular piece of dielectric material and electrode position. The definition of breakdown voltage is as follows:

Dielectric strength is a material property that describes the maximum electric field that a pure material can withstand until its insulating properties begin to fail. It's also known as the maximum voltage needed to cause a dielectric breakdown.

The dielectric strength is measured in Volts per unit thickness (V/m)\left( {V/m} \right) and is unaffected by the material or the electrodes that generate the electric field. It is a crucial property of an insulator, whose efficiency varies in direct proportion to the dielectric power.Dielectric strength means maximum electric field.
Unit of Dielectric strength =NC or Vm\dfrac{N}{C}\,or\,\dfrac{V}{m}
Dimensional formula=[N][C]\text{Dimensional formula} = \dfrac{{\left[ N \right]}}{{\left[ C \right]}}
⇒NC=M1L1T−2Q1 ⇒NC=M1L1T2Q−1\Rightarrow \dfrac{N}{C} = \dfrac{{{M^1}{L^1}{T^{ - 2}}}}{{{Q^1}}} \\\ \Rightarrow \dfrac{N}{C} = {M^1}{L^1}{T^2}{Q^{ - 1}}
∴NC=[M1L1T−2Q−1]\therefore \dfrac{N}{C} = \left[ {{M^1}{L^1}{T^{ - 2}}{Q^{ - 1}}} \right]
Dielectric dimensional formula =[M1L1T−2Q−1][{M^1}{L^1}{T^{ - 2}}{Q^{ - 1}}]

So, the correct option is A.

Note: Although they are connected, dielectric strength and dielectric constant should not be confused. The dielectric constant (also called "relative permittivity") is a dimensionless mathematical ratio of material permittivity to vacuum permittivity.