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

Option 1)

\left [ L^{-1}T \right ]

 Option 2)

\left [ L^{-2}T^{2} \right ]
Option 3)

\left [ L^{2}T^{-2} \right ]

 Option 4)

\left [ LT^{-1} \right ]

Answers (2)

As we learnt in Based on Formula: Permittivity of free space

\epsilon_{o}=\ M^{-1}L^{-3}T^{4}A^{2}^{}

 

wherein

CN^{-1}m^{-2}

and Based on Definition: Permeability of free space

Dimension of permeablity of free space (\mu_{o})-M^{1}L^{1}T^{-2}A^{-2} 

wherein

\frac{newton}{ampere^{2}},\frac{henry}{metre}

    

Dimension of the required quantity is : L^{2}T^{-2}


Option 1)

\left [ L^{-1}T \right ]

This is an incorrect option.

Option 2)

\left [ L^{-2}T^{2} \right ]

This is an incorrect option.

Option 3)

\left [ L^{2}T^{-2} \right ]

This is the correct option.

Option 4)

\left [ LT^{-1} \right ]

This is an incorrect option.

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Vakul

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