Question

If $ \mu_0 $ and $ \epsilon_0 $ are the permeability and permittivity of free space, respectively, then the dimension of $ \left( \frac{1}{\mu_0 \epsilon_0} \right) $ is :

• A. \( L T^2 \)
• B. \( L^2 T^2 \)
• C. \( T^2 / L \)
• D. \( T^2 / L^2 \)

Hint:

The dimensions of permeability and permittivity help determine the speed of light in a vacuum, and their relationship is key in electromagnetic theory.

Answer 1

The Correct Option is B

Using the formula, \[ C = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \Rightarrow 1 = C^2 = L T^{-2} \] Thus, the dimension of \( \frac{1}{\mu_0 \epsilon_0} \) is \( L^2 T^2 \).