Dimensions of `(μ₀ε₀)⁻¹ᐟ²` – Rankers Physics

Dimensions: Practice Problem & Solution

The dimensions of \((\mu_0\epsilon_0)^{-1/2}\) are: [2012 Mains]
\([L^{1/2}T^{-1/2}]\)
\( L^{-1}T \)
\([LT^{-1}]\)
\([L^{1/2}T^{1/2}]\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Dimensions. Understanding the underlying formula is key to arriving at the correct answer below:

The speed of light \(c = 1/\sqrt{\mu_0\epsilon_0}\). Therefore, \((\mu_0\epsilon_0)^{-1/2} = c\). The dimensions of speed are \([LT^{-1}]\).

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