In SI units, the dimensions of \sqrt{\frac{\epsilon _{0}}{\mu _{0}}} is :
 

  • Option 1)

    AT^{-3}ML^{3/2}

  • Option 2)

    AT^{2}M^{-1}L^{-1}

  • Option 3)

    A^{-1}TML^{3}

     

  • Option 4)

    A^{2}T^{3}M^{-1}L^{-2}

Answers (1)

\sqrt{\frac{\epsilon _{0}}{\mu _{0}}}=?

We know C=\frac{1}{\sqrt{\mu _{0}\epsilon _{0}}}

\left [ \epsilon _{0} \right ]=\left [ M^{-1}L^{-3}T^{4}A^{2} \right ]

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

\sqrt{\frac{\epsilon _{0}\times\epsilon _{0}}{\mu _{0}\times\epsilon _{0}}}=C\epsilon _{0}=\left [ M^{-1}L^{-3}T^{4}A^{2} \right ]\left [ LT^{-1} \right ]

\left [ \sqrt{\frac{\epsilon _{0}}{\mu _{0}}} \right ]=\left [ M^{-1}L^{-2}T^{3} A^{2}\right ]


Option 1)

AT^{-3}ML^{3/2}

Option 2)

AT^{2}M^{-1}L^{-1}

Option 3)

A^{-1}TML^{3}

 

Option 4)

A^{2}T^{3}M^{-1}L^{-2}

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