The B-H curve for __________ will be a straight line passing through the origin

Question

Examoogle · Accepted Answer

air

Explanation: The B-H curve (magnetization curve) represents the relationship between magnetic flux density ($B$) and magnetic field intensity ($H$). For non-magnetic materials like air, the permeability ($mu_0$) is constant, resulting in a linear relationship defined by $B = \mu_0 H$.

Working Principle: In vacuum or air, there are no magnetic dipoles to align, so the material does not exhibit saturation or hysteresis. Since the relative permeability $\mu_r$ of air is approximately 1, the flux density is directly proportional to the applied field strength. This leads to a constant slope on the B-H graph, which is represented as a straight line passing through the origin.

Key Formulas: $B = \mu H = \mu_0 \mu_r H$ — General magnetic relation; $B = \mu_0 H$ — Relation for air (where $\mu_r = 1$)

Key Points: Air is a non-magnetic material with a relative permeability ($\mu_r$) of 1.; The slope of the B-H curve for air is equal to the permeability of free space, $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ H/m}$.; Unlike ferromagnetic materials, air does not show saturation behavior.; The linearity indicates the absence of magnetic hysteresis.

Advantages: Predictable and linear response; No hysteresis or eddy current losses in air gaps

Disadvantages: Very low permeability compared to ferromagnetic cores; Requires much higher current to produce the same flux density

Applications: Design of air-core inductors; Magnetic circuit air gaps in transformers and rotating machines

Additional Info: Silicon steel, hardened steel, and soft iron are ferromagnetic materials; they exhibit non-linear B-H curves characterized by saturation and hysteresis loops.. The constant slope in the B-H curve of air is a fundamental assumption in solving magnetic circuit problems involving air gaps.

Answer: D is correct — The B-H curve for air is a straight line because air has a constant magnetic permeability, resulting in a linear relationship between $B$ and $H$.

Exam Tip: Always remember that ferromagnetic materials saturate, while linear materials like air and vacuum follow the simple linear relation $B = \mu_0 H$ regardless of the field intensity.

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