Question:
If \(\varepsilon_0\) and \(\mu_0\) are respectively the electrical permittivity and magnetic permeability of vacuum, the dimensional formula for \(\dfrac{1}{\sqrt{\mu_0 \varepsilon_0}}\) is
If \(\varepsilon_0\) and \(\mu_0\) are respectively the electrical permittivity and magnetic permeability of vacuum, the dimensional formula for \(\dfrac{1}{\sqrt{\mu_0 \varepsilon_0}}\) is
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Remember:
\[
c=\frac{1}{\sqrt{\mu_0\varepsilon_0}}
\]
So this expression always has the dimensions of velocity.
Updated On: Apr 29, 2026
- \(MLT\)
- \(MLT^{-2}\)
- \(ML^{-1}T^{-1}\)
- \(M^0L^1T^{-1}\)
- \(M^0L^{-2}T\)
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
We know:
\[
\frac{1}{\sqrt{\mu_0 \varepsilon_0}} = c
\]
where \(c\) is the speed of light.
The dimensional formula of speed is:
\[
[M^0L^1T^{-1}]
\]
Hence,
\[
\boxed{(D)\ M^0L^1T^{-1}}
\]
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