Math List-I with List-II.
List-I List-II
A) Capacitance, C (i) $M^{1} L^{1} T^{- 3} A^{- 1}$
B) Permittivity of free space, $ε_{0}$ (ii) $M^{- 1} L^{- 3} T^{4} A^{2}$
C) Permeability of free space $, μ_{0}$ (iii) $M^{- 1} L^{- 2} T^{4} A^{2}$
D) Electric field, E (iv) $M^{1} L^{1} T^{- 2} A^{- 2}$
Choose the correct answer from the options given below

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(A)-(iii),(B)-(ii),(C)-(iv),(D)-(i)

(A)-(iii),(B)-(iv),(C)-(ii),(D)-(i)

(A)-(iv),(B)-(iii),(C)-(ii),(D)-(i)

(A)-(iv),(B)-(ii),(C)-(iii),(D)-(i)

answer is A.

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Detailed Solution

Charge Q=CV $\Rightarrow C = \frac{Q}{V} = \frac{{(A \times T)}^{2}}{M L^{2} T^{- 2}} = M^{- 1} L^{- 2} T^{4} A^{2}$

Electric field, $E = \frac{F}{q} = \frac{M L T^{- 2}}{A T} = L M T^{- 3} A^{- 1}$

Force ,= $F = \frac{q_{1} q_{2}}{4 π \in_{0} r^{2}} \in_{0} = M^{- 1} L^{- 3} T^{4} A^{2}$

Speed of light , $C = \frac{1}{\sqrt{μ_{0} \in_{0}}} \Rightarrow μ_{0} = \frac{1}{\in_{0} C^{2}} = \frac{1}{[M^{- 1} L^{- 3} T^{4} A^{2}] {[L T^{- 1}]}^{2}}$

$= [M^{1} L^{1} T^{2} A^{- 2}]$

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