Question 123: Units , Dimensions and Error Analysis

Question

Dimension of $\frac{1}{\mu_{0} \in_{0}}$ should be equal to

Accepted Answer

The term $\frac{1}{\mu_{0} \epsilon_{0}}$ appears in the formula for the speed of light $c$, which is:
$c = \sqrt{\frac{1}{\mu_{0} \epsilon_{0}}}$
where $\mu_{0}$ is the permeability of free space and $\epsilon_{0}$ is the permittivity of free space.
The speed of light $c$ has dimensions of length over time ($\mathrm{L} / \mathrm{T}$). Therefore, the term $\frac{1}{\mu_{0} \epsilon_{0}}$ has dimensions equal to the square of the speed of light, which is $\mathrm{L}^{2} / \mathrm{T}^{2}$.

Answer

$\mathrm{T}^{2} / \mathrm{L}^{2}$

Answer

$\mathrm{T} / \mathrm{L}$

Answer

$\mathrm{L}^{2} / \mathrm{T}^{2}$

Answer

$\mathrm{L} / \mathrm{T}$

Units , Dimensions and Error Analysis

Dimension of \frac{1}{\mu_{0} \in_{0}} should be equal to

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