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

air

{"type":"technical","methodBadge":"Concept & Principle","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 $B = \\mu_0 H$.","workingPrinciple":"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.","diagramSvg":"B-H Curve for AirH (Magnetic Intensity)B (Flux Density)","keyFormulas":["$B = \\mu H = \\mu_0 \\mu_r H$ — General magnetic relation","$B = \\mu_0 H$ — Relation for air (where $\\mu_r = 1$)"],"keyPoints":["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, $\\mu_0 = 4\\pi \\times 10^{-7} \\text{ H/m}$.","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"],"comparisonTable":[],"additionalInfo":["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 $H$.","correctedOptions":["silicon steel","hardened steel","soft iron","air"],"coreConcepts":["Magnetic Permeability","B-H Curve","Non-magnetic materials","Linearity"],"crossTopicTip":"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."}