Dimension of \(\frac{1}{μ_0∈_0}\) should be equal to
- \(\frac{L}{T}\)
- \(\frac{T}{L}\)
- \(\frac{L^2}{T^2}\)
- \(\frac{T^2}{L^2}\)
The Correct Option is C
Solution and Explanation
Step 1: Use the relationship between µ0, ϵ0, and the speed of light.- Given $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$, we know:
$\frac{1}{\mu_0 \epsilon_0} = c^2$.
Step 2: Analyze the dimensions.- Dimensional formula for c: [c] = $\frac{L}{T}$.- Hence, $[\frac{1}{\mu_0 \epsilon_0}]$ = $[c^2]$ = $\frac{L^2}{T^2}$.
Final Answer: The dimension is $\frac{L^2}{T^2}$
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