Which of the following expressions is correct with respect to relative permeability?

Question

Examoogle · Accepted Answer

$B = \mu_r \mu_0 H$

Explanation: The magnetic flux density $B$ in a material is defined as the product of the absolute permeability $\mu$ of the medium and the magnetic field intensity $H$. Since absolute permeability is the product of relative permeability $\mu_r$ and the permeability of free space $\mu_0$, the relationship is given by $B = \mu_r \mu_0 H$.

Working Principle: In a magnetic material, an applied magnetic field intensity $H$ induces a magnetic flux density $B$. The constant of proportionality is the material's absolute permeability $\mu = \mu_r \mu_0$. The relative permeability $\mu_r$ represents how much more permeable a substance is compared to a vacuum (or air), scaling the magnetic effect.

Key Formulas: $B = \mu H$; $\mu = \mu_r \mu_0$

Key Points: $\mu_0$ (permeability of free space) is approximately $4\pi 	imes 10^{-7} 	ext{ H/m}$.; $\mu_r$ is a dimensionless quantity representing the ratio $\frac{\mu}{\mu_0}$.; For vacuum or non-magnetic materials, $\mu_r \approx 1$.; For ferromagnetic materials, $\mu_r \gg 1$.

Advantages: Allows simple calculation of flux density in magnetic circuits.; Provides a standardized way to compare magnetic properties of different materials.

Disadvantages: Assumes a linear relationship, which often fails in ferromagnetic materials due to saturation and hysteresis.

Applications: Design of electromagnetic inductors and transformers.; Calculation of magnetic flux in motor and generator cores.

Additional Info: The permeability of free space $\mu_0$ is defined as $4\pi 	imes 10^{-7} 	ext{ H/m}$.. Option A is incorrect as it introduces an invalid division by H, Option C incorrectly places $\mu_r$ in the numerator over $\mu_0$, and Option D incorrectly squares the magnetic field intensity H.

Answer: B is correct — The relationship between magnetic flux density, relative permeability, and magnetic field intensity is defined as $B = \mu_r \mu_0 H$.

Exam Tip: Remember that $\mu_r$ is unitless, making $B$ (in Tesla) proportional to $H$ (in A/m) via the units of $\mu_0$ (H/m or T·m/A).

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