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Limitation of Dimensional Analysis

The dimension...

Question

The dimensional formula of permittivity of free space is

M^{- 1} L^{3} T^{- 3} A^{- 2}

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M^{1} L^{- 2} T^{2} A^{2}

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M L^{- 3} T^{- 3} A^{2}

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M^{1} L^{- 3} T^{4} A^{2}

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Solution

The correct option is D $M^{1} L^{- 3} T^{4} A^{2}$
Unit of $ϵ_{0} is C^{2} N^{- 1} m^{- 2}$

$\Rightarrow [ϵ_{0}] = \frac{A^{2} T^{2}}{M L T^{- 2} L^{2}} = M^{- 1} L^{- 3} T^{4} A^{2}$

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