MCQ
Dimensions of $\frac{1}{(\mu_0\in_0)}$ is:
- A$\frac{\text{L}}{\text{T}}$
- B$\frac{\text{T}}{\text{L}}$
- ✓$\frac{\text{L}^2}{\text{T}^2}$
- D$\frac{\text{T}^2}{\text{L}^2}$
✓
Answer
Correct option: C.
$\frac{\text{L}^2}{\text{T}^2}$
The speed of light, $\text{C}=\frac{1}{\sqrt{\mu_0\in_0}}$
The dimensions of $\frac{1}{\sqrt{\mu_0\in_0}}$ are of velocity, i.e., $\frac{\text{L}}{\text{T}}$
Therefore, $\frac{1}{\in_0\mu_0}$ will have dimensions $\frac{\text{L}^2}{\text{T}^2}$
The dimensions of $\frac{1}{\sqrt{\mu_0\in_0}}$ are of velocity, i.e., $\frac{\text{L}}{\text{T}}$
Therefore, $\frac{1}{\in_0\mu_0}$ will have dimensions $\frac{\text{L}^2}{\text{T}^2}$
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