Question

The dimensional formula of dielectric strength
A. $M^1{L}^1{T}^2{Q}^{-1}$
B. $M^1{L}^2{T}^{-2}{Q}^{-1}$
C. $M^{-1}{L}^{-1}{T}^2{Q}^1$
D. $M^{-1}{L}^{-1}{T}^2{Q}^2$

Answer 1

Hint: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 $$\left(V/m\right)$$ 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 =${\displaystyle \frac{N}{C}}or{\displaystyle \frac{V}{m}}$
$\text{Dimensional formula}={\displaystyle \frac{\left[N\right]}{\left[C\right]}}$
$$\begin{gathered} \Rightarrow {\displaystyle \frac{N}{C}}={\displaystyle \frac{M^1{L}^1{T}^{-2}}{Q^1}} \\ \Rightarrow {\displaystyle \frac{N}{C}}=M^1{L}^1{T}^2{Q}^{-1} \end{gathered}$$
$\therefore {\displaystyle \frac{N}{C}}=\left[M^1{L}^1{T}^{-2}{Q}^{-1}\right]$
Dielectric dimensional formula =$[M^1{L}^1{T}^{-2}{Q}^{-1}]$

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.