Let [ϵ0] denote the dimensional formula of the permittivity...

Let $\left[\epsilon_{0}\right]$ denote the dimensional formula of the permittivity of vacuum. If $M=$ mass, $L=$ length, $T=$ time and $A=$ electric current, then (A) $\left[\epsilon_{0}\right]=\left[M^{-1} L^{-3} T^{4} A^{2}\right]$ (B) $\left[\epsilon_{0}\right]=\left[M^{-1} L^{2} T^{-1} A^{-2}\right]$ (C) $\left[\in_{0}\right]=\left[\begin{array}{ll} \left.M^{-1} L^{2} T^{-1} A\right]\end{array}\right.$ (D) $\left[\epsilon_{0}\right]=\left[M^{-1} L^{-3} T^{2} A\right]$

Let $\left[\epsilon_{0}\right]$ denote the dimensional formula of the permittivity of vacuum. If $M=$ mass, $L=$ length, $T=$ time and $A=$ electric current, then
(A) $\left[\epsilon_{0}\right]=\left[M^{-1} L^{-3} T^{4} A^{2}\right]$
(B) $\left[\epsilon_{0}\right]=\left[M^{-1} L^{2} T^{-1} A^{-2}\right]$
(C) $\left[\in_{0}\right]=\left[\begin{array}{ll} \left.M^{-1} L^{2} T^{-1} A\right]\end{array}\right.$
(D) $\left[\epsilon_{0}\right]=\left[M^{-1} L^{-3} T^{2} A\right]$

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Key Concepts

Dimensional Analysis

Dimensional analysis is a method used in physics to check the consistency of equations by comparing the units on both sides. It is utilized to derive units for physical quantities by expressing them in terms of base units like mass, length, time, and electric current, ensuring that equations are balanced dimensionally.

SI Base Units

The SI system relies on base quantities, including mass (M), length (L), time (T), and electric current (A), among others, to express the dimensions of physical quantities. Understanding these units is essential for converting and deriving the dimensions of more complex quantities, such as the permittivity of vacuum.

Vacuum Permittivity

Vacuum permittivity is a fundamental constant in electromagnetism that characterizes the ability of free space to permit electric field lines. Its dimensional formula is derived from the relationships in Coulomb's law and connects electric quantities to mechanical dimensions, thereby playing a key role in the analysis of electromagnetic interactions.

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