Question

Unit of \( \frac{{\mu_0}}{{\epsilon_0}} \) is.

• A. newton/coulomb
• B. ohm
• C. henry
• D. farad

Hint:

The characteristic impedance of free space, \( \frac{{\mu_0}}{{\epsilon_0}} \), has the unit of ohms, which is the unit of electrical resistance.

Answer 1

The Correct Option is B

Step 1: Understanding the quantity.
The quantity \( \frac{{\mu_0}}{{\epsilon_0}} \) is known as the characteristic impedance of free space, where \( \mu_0 \) is the permeability of free space and \( \epsilon_0 \) is the permittivity of free space. The value of \( \frac{{\mu_0}}{{\epsilon_0}} \) is used in the calculation of the speed of light in vacuum and is related to the unit of resistance, which is ohm.
Step 2: Relation to other units.
The unit of \( \frac{{\mu_0}}{{\epsilon_0}} \) is derived from the formula \( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \) and \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N·m}^2 \). Combining these gives the unit as ohm (\( \Omega \)), the unit of electrical resistance.
Conclusion: The unit of \( \frac{{\mu_0}}{{\epsilon_0}} \) is ohm.