What is the relative permeability of a vacuum?

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Explanation: The relative permeability ($\mu_r$) is a dimensionless parameter that represents the ratio of the permeability of a substance to the permeability of free space (vacuum). By definition, the permeability of a vacuum ($mu_0$) is taken as the reference, thus making the relative permeability of a vacuum exactly 1.

Working Principle: Permeability ($mu$) characterizes how a material responds to an external magnetic field. The relationship is defined as $\mu = \mu_0 	imes \mu_r$. Since for a vacuum, $\mu = \mu_0$, it follows mathematically that $\mu_r = \frac{\mu_0}{\mu_0} = 1$.

Key Formulas: $\mu = \mu_0 \mu_r$ — Relation between absolute, vacuum, and relative permeability; $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ H/m}$ — Permeability of free space

Key Points: Relative permeability is a dimensionless scalar quantity.; For diamagnetic materials, $\mu_r; For paramagnetic materials, $\mu_r > 1$ (slightly greater than 1).; For ferromagnetic materials, $\mu_r \gg 1$.

Advantages: Simplifies calculations in electromagnetic field theory by using constants.; Provides a standardized reference scale for comparing different magnetic materials.

Applications: Design of inductors and transformers.; Electromagnetic shielding analysis.; Magnetic circuit calculations.

Additional Info: The value $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ H/m}$ (Option D) is the absolute permeability of a vacuum, not the relative permeability.. Option B (1 H/m) is incorrect as permeability has units, whereas relative permeability is unitless.

Answer: A is correct — The relative permeability of a vacuum is defined as the ratio of its own permeability to itself, which is exactly 1.

Exam Tip: Always distinguish between absolute permeability ($\mu$, units of H/m) and relative permeability ($\mu_r$, dimensionless). Confusing these two is a common source of errors in competitive exams.

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