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The dimensions of $(\mu_0\varepsilon_0)^{-\frac{1}{2}}$ are
A
$[L^{-1/2}T^{1/2}]$
B
$[L^{1/2}T^{-1/2}]$
C
$[L^{-1}T]$
D
$[LT^{-1}]$
Detailed Solution
The speed of light in vacuum is related to the permeability and permittivity of free space by $c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}$
So $(\mu_0\varepsilon_0)^{-\frac{1}{2}} = \frac{1}{\sqrt{\mu_0\varepsilon_0}} = c$
The given expression is therefore a speed, and speed = distance/time.
Dimensions of $(\mu_0\varepsilon_0)^{-\frac{1}{2}}$ = $[LT^{-1}]$
So $(\mu_0\varepsilon_0)^{-\frac{1}{2}} = \frac{1}{\sqrt{\mu_0\varepsilon_0}} = c$
The given expression is therefore a speed, and speed = distance/time.
Dimensions of $(\mu_0\varepsilon_0)^{-\frac{1}{2}}$ = $[LT^{-1}]$