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Derived Quantities

Dimensions of...

Question

Dimensions of 1/(µ₀ϵ₀) is
(a) L/T
(b) T/L
(c) L²/T²
(d) T²/L².

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Solution

(c) L²/T²

The speed of light, $C = \frac{1}{\sqrt{μ_{0} \in_{0}}}$ .
The dimensions of $\frac{1}{\sqrt{μ_{0} \in_{0}}}$ are of velocity, i.e. L/T .
Therefore, $\frac{1}{\in_{0} μ_{0}}$ will have dimensions L²/T².

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