Question

Dimensions of$\frac{\mathbf{1}}{\mathbf{\mu}_{\mathbf{0}}\mathbf{\varepsilon}_{\mathbf{0}}}\mathbf{,}$ where symbols have their usual meaning, are

• A. $\lbrack LT^{- 1}\rbrack$
• B. $\lbrack L^{- 1}T\rbrack$
• C. $\lbrack L^{- 2}T^{2}\rbrack$
• D. $\lbrack L^{2}T^{- 2}\rbrack$

Answer 1

Answer: (D)

$\lbrack L^{2}T^{- 2}\rbrack$

Answer 2

We know that velocity of light $C = \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}}$

$\therefore$ $\frac{1}{\mu_{0}\varepsilon_{0}} = C^{2}$

$\therefore$ So $\left\lbrack \frac{1}{\mu_{0}\varepsilon_{0}} \right\rbrack = \lbrack LT^{- 1}\rbrack^{2}$ = $\lbrack L^{2}T^{- 2}\rbrack$.